As others have said this is a spurious claim. A simple google search reveals that the population of the Thirteen Colonies in 1776 was ~2.5 million. Three percent would be 75,000. Even a cursory look at wikipedia's entry on the Revolutionary War, mentions that over 250,000 men fought as regulars or militiamen at some point during the conflict, although the standing size of the Continental Army never exceeded 90,000.

My guess is that someone took the size of the Continental Army at some point in the conflict when it was roughly 75,000 and divided that into 2.5 million and came up with the figure of only 3% of Americans fought. In reality, the percentage would be closer to 10% and as others have stated, that doesn't account for who was actually being counted in the 2.5 million total, or who was capable and willing to fight based on gender, age, race, etc.

When you consider that only around 50% of 'Americans' were available for service on the basis of gender, and then that percentage is further reduced to males 'fit for military service', i.e. Precluding the young, the old, the infirm, then you're left with a much smaller percentage to draw recruits from for potential military service. I'd be highly skeptical about any figure related to military service that takes stock of an entire population if it includes females.

Furthermore, consider that a portion of the population is loyalist, or in areas under British control where it would be difficult to join the Continental cause because that necessitates a lot of travel and risk of your family and your property's well-being, since both are left in British hands.

Consider also that African-Americans may also be included in your total population, where many are enslaved and most wouldn't be able to join the army anyways.

So when you start paring away pieces of that 100% who couldn't or wouldn't be expected to fight, that 3% of the total becomes meaningless, if its true to begin with. Furthermore, the size of any Continental Army was always limited by Comgresses ability to pay and supply the men with spotty contributions and taxation.

What is relevant to your 2nd Amendment discussions is that in a primarily agrarian society, a large portion of the available male population left their farms and their families to fight in the war, many doing so armed only with the weapons they hunted and protected their homes with - at least to begin with.

I'd be interested to hear where you heard the 3% figure, or if there's a source. But if it's being used as a justification to say the 2nd amendment is a fraud, I'd call the statistic extremely misleading and likely dishonest without knowing more about it.

So I see the figure is spurious, but it might be worth pointing out that 3% is not really an "only" when it comes to mobilising a percentage of the population. In total-war conditions with twentieth-century wealth, the Great Powers managed to put perhaps 10% of their populations into uniform (although of course many more supported the war in industry and such).