Because 80 per cent of the Republicans in the House of Representatives don't have to worry about what the general public thinks. They represent congressional districts that have been so shamelessly gerrymandered by state legislatures that it is almost impossible for anybody who is a Republican to lose an election there. National public opinion is no threat to them, whereas the views of their extremist Tea Party colleagues are a potentially lethal danger.
You can't gerrymander the Senate; every senator's "district" is the entire state he or she represents. State legislatures controlled by the Democrats also gerrymander congressional districts to create safe seats for their own party, but there is no organised extremist group in the Democratic Party that will try to destroy elected members of their own party.
Republicans seeking re-election to the House of Representatives may not have to worry about their Democratic opponents, but they certainly have to fear the Tea Party. If it decides to mount a challenge to an incumbent in the Republican primary elections, the far-right challenger will be lavishly funded by the Tea Party's wealthy supporters, and that may mark the end of the incumbent's political career.
So the Republicans in the House of Representatives, even those generally open to compromise, are keeping their heads down for fear of angering the Tea Party. That means it is possible (though not probable) that the October 17 deadline will be missed, and the US Government will be forced to default on its debt. How bad would that be?
Very bad, according to a US Treasury spokesman. "Credit markets could freeze, the value of the dollar could plummet, US interest rates could skyrocket, the negative spillovers could reverberate around the world." And it might rain frogs and blood.
Or maybe not. There would certainly be turmoil in the markets: many people would lose money, and some would gain. But it would not be a repeat of the crash of 2009, when it was suddenly understood that huge amounts of the mortgage debt held by banks could never be repaid.
The US Government can still pay its debts; it just has to get Congress' permission first. And the markets, while prone to panic, are not completely stupid.
Nor is the US Constitution fundamentally broken. It always requires a fair degree of compromise between the various branches of the Government in order to work smoothly, and at most times in history that co-operation has been forthcoming.
The current paralysis is due mainly to the gerrymandering of congressional districts that makes members of the House of Representatives less afraid of public opinion than of the views of their own party's hardliners.
It wouldn't hurt to put some controls on election spending as well, so that rich ideologues had less influence. But that is merely desirable; ending the gerrymandering is absolutely essential. It will take time, but this is a problem that can be fixed. And in the meantime, the US Government is not really going broke.