"Bailing out" Americans by sending them a large check would be irresponsible, short-sighted, and destructive. Americans can't control their spending habits as it is, much less with thousands of dollars in government cash burning holes in their pockets. People would get themselves current on their bills, and then splurge because they "deserve it."
I liken it to the episode of Oprah or Dr. Phil (can't remember which) on which a documentary filmmaker gave a homeless guy $100,000 just to see what he would do with it. He blew it all within like three months of getting it. He had no idea what to do with that much cash, and neither do most Americans.
So what would happen when the money ran out? Sure, you've "stimulated" the economy by spending money, but all that does is transfer wealth from the government to private industry. If I recall correctly, that is what most people complain about when talking about those evil CEOs and their big paychecks. Where do you think that money comes from?
Not to mention the inflation that would occur from every American having all of that money to spend. Prices on every luxury item would be out of control because of ridiculous Americans going out to buy that "one thing they've always wanted." The only way you could equitably "bail out" the American public and not have it result in mass ridiculousness would be to buy certain classes of American debt (which is an awful idea all on its own) in an effort to level the playing field again. None of it will happen because the government knows that they can't trust the American public with $10 much less $10,000.
If you think the government is bad at managing money, just take a look around at all of the people who have gotten themselves into these financial messes in the first place. Sure, fueling the fire by giving these people money (and thus indirectly validating their idiotic behavior) is the answer. No way.