Not ASB at all. What people seem to forget is that although the British had the largest Navy and a good Army, they also had interests spread around the world. The Britain of the mid 1800s (which is when I would assume this would take place) couldn't very well pull troops out of India or Ireland or they'd be facing revolt on their hands.
On the other side, you only need to look at the Civil War to see the kinds of men the United States could muster when it wanted to. In addition, the British are not going to be able to blockade any post Mexican-American War USA with impunity- it's a long coastline with a lot of production. And again, the British have to protect their interests elsewhere.
So once you get into the mid-1800s, the Americans can win this hypothetical War handily- because Wars do not exist in a vacuum.
What do you mean, pull troops out of Ireland? Ireland was really very placid (relatively speaking) in this time period, and indeed provided large numbers of volunteers for the armies of Empire.
And the British
home army (not in the colonies or in India) was quite large, as was the Militia (think national guard, complete with wholesale enlistment in the regular army under wartime conditions.)
Thing is, any pre-1860s war would result in the South going gaga. (Expansion of free soil?) And 1860-1890 the US's problem is that the Brits have a
huge navy without trying financially.
To give some idea of how much the UK was coasting during the 1860s, in terms of funding, the Crimean War and Indian Rebellion debt was
so very paid down ~1860 that Palmerston seriously considered abolishing income tax for simple lack of need.
By contrast, the US debt from the ACW took decades to painstakingly pay down. (Mainly by growing the economy so the % of GDP went down.)