Since the U.S. bonds are all denominated in the same money that it controls, and the federal government has huge assets and potential revenue streams, I'd put a risk of default quite low; low enough to get an AAA, anyway.
The federal government pretty much can't default unless it actively chooses to, given the huge number of options for servicing debt at its disposal (cutting spending elsewhere, raising taxes, printing money, selling land). So it's almost entirely a political question of how high you think the chances are that the government will choose to default rather than use one of the other options. I would rate that pretty low. But it's not really an actuarial question either way; it's a guess about policy.
But that is exactly why they downgraded us. Given everything you listed, we still were within days of default, thanks to how paralyzed the political process has become in Washington.
We were within days of the debt ceiling, not of default. Plenty of things could have been shuffled around to meet all debt payments (including some politically useful ones like stop sending SS checks, don't pay the troops, etc).
It depends on what you mean by "debts"; you're only in default from the finance industry's perspective if you fail to service bonds/loans/etc., not if you fail to make other payments you've promised. For example, if IBM stopped paying its employees' salaries, or stiffed its suppliers, but continued servicing its bonds, it wouldn't be in default. S&P is specifically rating the chance of a default on bonds.
Actually I don't think this is the case. The US uses treasury bonds like you or I would use a credit card, they sell bonds take the money and pay bills. They pay them off by exchanging them for cash at a later date. So essentially when we're at the debt ceiling we nominally can't sell any more t-bills so the only money the government has available is money from revenues coming in. Pretty much instantly forced to live without your credit card.
Now since the current budget actually spends more than is expected in receipts, that means things that were already approved and budgeted would not have the funding to pay for them. But in the unlikely event that the debt ceiling had not been raised the government would switch to a priority system of paying (effectively cutting spending).
Its my understanding that at no time has the US ever been at risk of 'default' in the sense that a bank wants its money and the holder of the note can't pay. But it might have been in danger of suddenly withdrawing from Iraq and Afghanistan. Since at 2 B$/day (one estimate I've heard) that is over 700B$/yr of money we would probably prioitize not to spend.
The federal government pretty much can't default unless it actively chooses to, given the huge number of options for servicing debt at its disposal (cutting spending elsewhere, raising taxes, printing money, selling land). So it's almost entirely a political question of how high you think the chances are that the government will choose to default rather than use one of the other options. I would rate that pretty low. But it's not really an actuarial question either way; it's a guess about policy.