The State militias, which the US largely relied on, were ... variable, shall we say.
While it's true that the Kentucky mounted militia was very effective, most of the other States' militias were ineffective for an invasion.
Militias were raised to DEFEND, and militia men were meant to defend their own state. In the War of 1812, militiamen asked to cross the international border often said 'no, we don't have to, and we're not going to'. Heck, some militia refused to go further than the next State over. Worse, to some extent worse, each man made his own decision, so unit cohesion broke down. Officers had to convince and cajole their men into obeying orders (especially ones the men weren't obliged to follow).
It also didn't help that much of the Army high command were doddering incompetents.
If you could convince the 13 states that their militias were useful only as back up, and that a standing army really was necessary, well then you'd have a bigger army, more trained officers, and you could dump the deadwood at the top.
It would also help if there was any kind of concept of logistics.
If the US had had a decent, professional army, and if they'd, for instance used Lake Champlain as a supply route to seize chunks of Quebec province, cutting British supply to Ontario, they could have won handily.