So, the first issue was that America had state militias and the Continental Army. The states were responsible for raising, maintaining, and paying for the militias, and they were also responsible for sending funds to the Continental Congress to maintain the army. This goal was that the Continental Army would form the nucleus, and be supplemented by the State militias - the army would have longer enlistment periods and be paid, the militia would be more ad hoc and either not paid or paid less.

So, the first way you got people into the army was promise of higher pay, and by talking up patriotism. The army also commissioned a lot of state militia officers - most of the initial line officers had been in their state's militias, for example. In the North, slaves were promised their freedom, and up to a fifth of the army in the North was black - this promise was generally not available in the South. And there was begging. A lot of begging.

In The Glorious Cause, Robert Middlekauf's estimate was about 1/3rd Patriot, 1/3rd Loyalist, and 1/3rd neutral, with those numbers moving around based on location, Patriot excesses, and British excesses.

The real problem wasn't that the "average joe" didn't care about being independent. It's that when push came to shove, "average joes" would wander off. Merchants would send the first shipment of supplies they promised, but not the third. The militias were hit harder due to shorter periods - but even the Continental Army had a massive problem with desertion, especially during periods such as Valley Forge (when they nearly froze to death), and the late part of the war (1780-81) when pay and supplies were chronically short. The states would scream for help and pour men for their own defense, and when the British marched somewhere else, they slacked off. Or, in Benedict Arnold's case - patriotism waned when people felt their very real sacrifices weren't being taken seriously. To make matters worse, Washington consistently found himself near a battle with his men hitting the end of their enlistment periods, and he was often entreating his men to hold on to the end of the campaign.

This is one of the reasons for the following quote: "To place any dependence upon militia, is, assuredly, resting upon a broken staff. Men just dragged from the tender scenes of domestic life - unaccustomed to the din of arms - totally unacquainted with every kind of military skill, which being followed by a want of confidence in themselves when opposed to troops regularly trained, disciplined, and appointed, superior in knowledge, and superior in arms, makes them timid and ready to fly from their own shadows." - Letter to the president of Congress, Heights of Harlem (24 September 1776)

The long term problem was that Congress understood on one hand that they needed a well-trained, disciplined army to beat the British, and that the militia simply wasn't up to sustained campaigning. They also were terrified of a standing army and felt it was the biggest threat to their fledgling nation (which they almost found out in 1783 after not paying it). This problem continued through Shay's Rebellion, the Whiskey Rebellion, the Northwest Indian War, and the War of 1812, where the desire not to have a standing army and the desire not to lose were often in conflict.

This is a question I'd like to see answered as well. Some follow-up:

The Continental Army was formed in June 1775. That was over a year before the 2nd Continental Congress passed a resolution declaring independence, nearly a year before any of the local independence movements really got going, and half a year before Thomas Paine got the nerve to tell everyone they didn't need a king. It was even several months before George III declared the American colonies out of his protection, sending a fleet to pacify them.

So, at the time of the formation of the Continental Army, it seems to me that the "American Revolution" basically amounted to a few clashes in & around Boston, between British soldiers and mobs angry about taxes.

Just what the heck was the Continental Army for, in June 1775?

And why was George Washington in charge of it? I'm familiar with John Adams's line about a Virginian needing to be seen at the head of this thing. But what was "this thing" in June 1775? Why should a Virginian be leading a Massachusetts tax revolt?

The importance of pay can't be emphasized enough. In my opinion, the paying of bounties was probably the largest single factor in inducing men to enlist in the Continental Army. I know the most about the situation in Virginia, where service in the Continentals remained wildly unpopular for most of the war - much to the embarrassment of General Washington, who complained vociferously each time Virginia fell short of her quota.

While middle- and upper-class citizens were willing to serve in the Continental Army as officers, very few were interested in becoming rankers. This did not necessarily mean that they were unpatriotic. The larger British world shared a common prejudice against ordinary soldiers. Military service was associated with the lowest classes - drunkards, scoundrels, petty criminals, the indigent, and the like. It was not a place that a "decent" man wished to go. Propertied men much preferred to remain at home, either as part of the general militia - which is to say, expected to do nothing until called up in event of an emergency - or in one of the companies of "minutemen," a special subset of the militia held in better readiness.

As such, Virginia concentrated recruitment efforts on the poor. The paying of bounties - that is to say, a lump sum of cash or land - was the most reliable and frequently used method of inducing men to enlist. But as the war dragged on, it became more and more difficult to raise troops by this method. Towards the end of the war, the bounty grew well over $1,000 - a very large sum for the time. But even very large bounties were not always enough to induce men to risk life and limb, and as such, Virginia attempted on several occasions to institute limited conscription - a draft, based on county quotas. This was not at all well received, and resulted in rioting, disorder, desertion, and the like. Ultimately, the bounty was the only reliable method of meeting Virginia's military commitment.