It's unlikely in the
extreme that there'd be anything approaching a land raid on Britain, let alone a land invasion. There's no real capacity for it in any sense.
Now, if we look at the Crimea we can see examples (Kinburn and indeed the entire Sea of Azov) of a fort being defeated by bombardment.
I think it's unquestionable that a long enough bombardment against any fort can dismount or render unusable any guns mounted
en barbette, and that heavy enough guns can chip away at and damage/destroy the fortifications themselves. (The high velocity 68-lber guns on the Terror and other ironclads, fired from close in, can almost certainly smash a masonry fort quite quickly.)
Most of the forts protecting NY have large fractions of their armament mounted en barbette, so a day or so of bombardment would reduce them to just the casement guns - a relatively small fraction of the total possible.
As for mining or sinking obstructions, they're both possible but the RN has been planning to deal with them for years or decades. (Years for the mines, decades for the sunken obstructions.) And a mined-up and blocked port is useless for trade anyway.
Here's what happened when the British first ran into mines.
The mines were close to the surface and could usually be seen and recovered with grapnel lines. In seventy-two hours of this, the world’s first minesweeping operation, thirty-three infernal machines were recovered.
These were the more effective contact mines; they also had electrically-detonated mines, which were less effective. If the US wants to use electrically detonated mines on the British they'd have to build fortified defences for the operators - which takes time, certainly longer than a few weeks.
Adding to this is that OTL the US didn't even bother trying to start laying large belts of mines during the tense period between Trent and the climbdown - they didn't even
plan for what to do.
Think about that for a bit. The Trent took place on November 8. The news hit the US on the 16 November, and from then to the 30 December the main things the US did to prepare for a war were... very little.
The news got to the UK on the 27 November, and from there to the 30 December the British send an ultimatum, move troops, send out weapons, rush modern ships to the theater, issue conditional war orders and write up a detailed defensive plan
based on the worst case scenario:
27th November 1861: News of the seizure reaches the UK
29th-30th November 1861: Special War Cabinet sits, UK ultimatum sent to the Federal States
4th December 1861: Mobilisation is ordered.
7th December 1861: The
Melbourne, carrying large quantities of munitions and the first British reinforcements departs. The
Orpheus, 21 escorted her from Plymouth.
9th December 1861: 25,000 men are ordered to Canada
10th December: Correspondents at Malta report the Mediterranian squadron has been ordered to dispatch all disposable ships to North America
16th December: RAdm Dacres appointed second in command to VAdm Milne, his flag is the
Edgar, 89
19th December 1861: The first two battalions of Lord Frederick Paulet’s 1st Guards Brigade embarks for Canada (having had 6 days notice), the 3rd battalion (2nd Coldstreamers) is not embarked before the crisis abates.
20th December 1861: Williams issues General Militia Order No. 1, embodying a company of 84 offrs and men from each battalion of the Service Militia (roughly 38,000 men, exc/ offrs and Bn staffs), to be ready to march 14 days after recipt of the order.
21st December 1861: The gunboat reserve is activated
(and then the climb down happens)
So the US had 50 days or more and did very little. The British had 35 days, and moved 20,000 or so troops (counting cavalry and artillery) plus 40,000 modern rifles for the Canadian militia, over 2.5 million rounds of ammunition and at least 66 guns more modern and accurate than anything the US has.
My point here is that I don't think the US would have been able to use their remaining time as well as the British were. The Union had already wasted seven weeks, I doubt they could go from that to setting up an idealized defence plan of NY in the remaining eight. (While the British consider attacking ports to be sensible doctrine.)
I won't even bother addressing the question of a defensive fleet because the US doesn't
have a fleet worth a damn. They have Monitor, four screw frigates, some sloops, and some increasingly less effective paddle/sail sloops and converted merchant ships. Nothing -
nothing - except Monitor and the screw frigates can even hope to stand up to a 51 let alone a 90 or 120 - and those screw frigates and screw sloops are essentially their only hope for commerce raiding.
I'd also like to address the idea of rapidly moving in reinforcements to areas which are at risk of amphibious descent. I think the example of Washington DC in 1861 demonstrates that this is not possible on a short timescale.
Crimea was the first British experience landing on enemy soil in about 50 years. Despite this, they fought at the Alma a week after landing at Calamita Bay, 35 miles away from Sebastopol. Given how long it took to get troops to Washington in 1861- Lincoln calls for reinforcements on 15 April and by 26 April there are only four regiments there - it seems likely that the expected ability of the US to reinforce the coastline depends on actually having that coastline already garrisoned.
If we assume that it would take a week for the Union to rush forces to a threatened location - which is
extremely generous given the 1861 example - then the question becomes either:
1) Can the Union spare enough troops to garrison the coastline thickly enough to prevent a British landing? (I'd expect at
least 35,000 troops and 120 guns to be necessary to prevent a full-court British & French attack - they beat that many at the Alma - and there's several locations to defend)
2) Can the British reduce the forts and take New York inside a week?
(1) is certainly possible, though it would basically take 100,000 troops just to defend Bostom + The Delaware + New York, and that's a low estimate - and it comes out of an army already having force allocation problems, reducing their ability to both continue fighting the CSA and invade Canada.
Note that this is in addition to the troops operating the guns - 600 spare fortress guns means about 6,000 extra gunners, plus various ancillaries, and most of the east coast forts with guns in aren't manned as of the PoD - but I'm assuming they are.
But if they don't do that, then (2) there's the other problem. Which is that I think the New York forts would be lucky to hold out more than two or three days against a combined bombardment and landing. This is giving them a lot of credit - Kinburn was about as heavily armed as the entire New York Narrows system and it held out roughly three hours, I'm assuming about nine times as long.
The fort was of masonry with an earth parapet and mounted sixty guns in casemates and about twenty more in barbettes. There were also two powerful open batteries.
Brown , David K (2015-09-09). Before the Ironclad: Warship Design and Development 1815-1860 (Kindle Locations 4993-4994). Seaforth Publishing. Kindle Edition.
This isn't the only time - Sveaborg had magazine explosions after three and four hours of bombardment by mortar vessels, and they destroyed the storehouses by the end of the 12th.
The British had 106 mortar vessels built during the Crimean War.
So it'll probably have to be garrisons.
Speaking of force allocation, since it's come up just now - here's the problem the US has.
In OTL they had a certain allotment of forces. They have roughly speaking four troop sources:
1) Existing infantry units that are in field armies.
2) Existing infantry units in forts.
3) Existing infantry units still in training.
4) Newly raised infantry post-PoD.
And artillery-wise they have a similar situation.
i) Artillery in field armies.
ii) Artillery in land forts.
iii) Artillery in coast forts.
iv) Reserve artillery.
v) Artillery in ships.
The requirements here are:
A) Keep fighting the Confederacy.
B) Garrison the coast.
C) Provide a field army to invade Canada.
C) requires around 200,000 troops - which is what the British mobilization was expected to be able to counter. (A) requires most though not all of the troops currently involved, and (B) needs either a few troops or lots of them depending on how hard you want to do it. (If you're comfortable letting the RN have most of the coast, you can get away with defending Delaware River plus Boston plus NY plus Washington - meaning 100,000 troops.)
Here I won't even get into if there's the rifles required, but I think the evidence is incontrovertible from OTL that a lot of these troops - much like OTL - are going to be armed with muskets.
Troop wise, (1) and (2) are effectively committed - you can free up a few divisions by cancelling things, a few more by going to a defensive posture, but it's going to cripple the offensives planned for 1862. This could free up - round number - 50,000 troops (which is IMO generous.)
That means you need 250,000 troops from (3) and (4). Troops in (3) are going to be new and unskilled but at least reasonably trained, troops in (4) are going to be roughly as green as Canadian Militia are at that same point in time.
I think the likely situation is that at most half the troops can be from (3) - so the average force doing jobs (B) and (C) is going to be ~20% experienced, 40% inexperienced and 40% recruit.
As to artillery, there's a similar situation - you can't get much from (i) and (ii), they're already fighting the CSA. (iii) is actually an artillery sink, many forts are
undergunned, so you'll be drawing heavily on the 600 guns in (iv) to supply artillery for the coastal forts. (they're too heavy for service in field armies.) Those 600 guns will, based on the known sample, get you 200 flank howitzers, 300 32-lbers and 100 24-lbers - after that you're out of luck - and roughly a quarter of that will arm two or three forts total.
(v) is actually quite tempting at this point...
In any case. If the Union does manage to fortify its coast to the point the British can't strike at NY or up the Delaware, it's going to have to commit almost everything it's got to spare and reduce forces in the south. 200,000 extra troops to invade Canada are going to be almost entirely musket armed raw recruits, and they're going to be facing a force which is about 2:1 composed of "militia with as long training as them if not a few weeks longer and armed with Enfields" and "heavily experienced crack shot British Regulars".
The Union
may be able to manage the job of keeping their coastline secure, invading Canada successfully and still avoiding losing to the CSA. But it's going to be a considerable uphill struggle, and they may need to pick which
two they'd prefer - and even then, a full-court British attack on New York is going to be very hard to counter.
And
none of this prevents a British blockade. The Union simply does not have the tools required to prevent a close blockade - consisting of either a battlefleet, large numbers of torpedo boats, or large numbers of submarines.
So the
best case for the US is a large army, not much better trained than the army that fought Bull Run, invading Canada; a series of inconclusive bombardments on their fortifications; a blockade; and the Confederacy pretty much sitting pretty.
The
worst case is that the powder mills are lost; no troops in reserve if an army in contact with the CS suffers a reversal; all the US dockyards on the East Coast destroyed with their building ironclads; no surviving navy; no purchases of weapons from Europe... and most of their merchant fleet either reflagged or seized.
Given that, it's easy to understand why the US backed down.