I don't think anyone has claimed that Britain "is just going to sit back," what I have implied is that I don't think the British have a way to seriously disrupt an American mobilization and once both sides mobilize you have a total-war between the two largest economies in the world. My refrain is that this war would be an endless quagmire to seemingly no useful end. Nothing posted has dissuaded me of this opinion.
No, it's not a magic wand, I'm not saying it is, but it is important. Historically, even in the Crimean War, the British had "interior lines" by virtue of naval superiority and the ease and speed of transport over water as opposed to land. In this case, the U.S. has the interior lines thanks to its robust system of railways and canals. Also, as shown in the Civil War, the U.S. can certainly leverage its industrial capacity over time. It's weird to me that argument comes down to a country with a small standing army (U.K.) absolutely trouncing a country with a miniscule standing army (U.S.A.) before either side has a chance to mobilize. No one has the forces to do much of anything before the first winter, and then we get into the both sides calling up militia and off to total war we go, a total war that becomes this huge pointless quagmire I keep bringing up.
Once again, the plan laid out by the pro-British posters in this thread is that British forces will launch a series of widely dispersed offensives across multiple states with minimal forces and mount naval raids against major coastal cities - raids that seem in all regards the 19th century equivalent of terror bombing. We know historically that terror bombing a peer industrial power serves only to piss off that power and harden their resolves (the Blitz is a good example of this). So that's likely going to make the war longer rather than shorter. Likewise the sort of rapid "shock-and-awe" style offensive against an opponent- an opponent with superior interior lines and ease of transport - is just asking for disaster, considering the distances required and massive logistical constraints.
The blockade will certainly be effective to an extent, but unless the entirety of the Royal Navy is committed, there's no way to lock down the whole of the U.S. east coast from Texas to Maine. That's roughly equivalent to the Atlantic and Mediterranean coasts of Europe, from Copenhagen to Athens.
So, in summary, I don't think the British have the standing forces to win a continent sized war in less than 6 months. After that it's a total war between two massive economies, with guns, people, and natural resources to spare. I do not see a good argument to the contrary besides the sort of jingoistic attitude that "my country has the strongest, tallest most determined people and all other countries are run by spineless puddles of men."