The ability of both sides to mobilise is a known.
In 1898 the US mobilised for their war with Spain. Apart from their small regular army it was found that only 60,000 of the 100,000 nominal NG had ever attended drill, let alone shouldered a rifle. They had no modern artillery (even the regulars still had a black powder gun not much more advanced than those of the ACW) and were using converted ACW era Springfields as their shoulder arm.
In 6 months they raised an army of 275,000, but only the regulars and a small number of NG (mainly from NY, which had a very efficient NG) were ready for the field.
Faced with South Africa, the British sent 238,000 regulars (inc. regular reserves), 18,000 Indians, 110,000 British reservists (volunteers, militia and yeomanry), combined with 30,000 from Canada, Australia and NZ and 52,000 South African troops.
In the event of a major war, Britain can place over 300,000 troops into Canada, in addition to the 200,000 Canada can be expected to field. Any ideas of overwhelming US numbers are based on a very prolonged war, which the US will have a great deal of trouble prosecuting (as their coastal cities burn, their main war industries are destroyed, and a British blockade makes the production of war material impossible).
For the US to win a war against the UK before 1914 (perhaps even later) they need to win quickly.
Finley explicitly pointed out that Britain and the US already fought a war in 1838 and the latter wants 'revenge'; it is not, therefore, terribly improbable that the US has a larger regular force, a larger reserve force, and has better equipment and training for both. Similarly, it is likely that such a US WOULD participate in the Dreadnought race, and would have more formidable coastal defenses than OTL, so total superiority of the RN is not as much of a given as it was OTL at this period.