I'll begin with some quotes from a previous post of mine, dating from last February: Reading the Tea Leaves.
[The Tea Partiers] have an Ace up their sleeve -- so they think. If the Democrats won't cooperate, they'll make sure the debt limit isn't raised, which [requires] Republican votes -- lots of them. And if the debt limit isn't raised, why, it will be the end of civilization as we know it. Which is fine with them. Also fine with me, by the way.
Unfortunately for our eager beaver Tea Partiers, it will NOT be fine with the oligarchs whose big money got them to Congress in the first place. Because if the national debt limit isn't raised, the USA will go into default and if the USA defaults, then a whole lot of very wealthy people will be in danger of losing a whole lot of their wealth. . .Thus, as I see it, there is no way the Tea Party could maintain its grip on the Republican power structure if they were to vote down a simple yea or nay bill to raise the debt ceiling. Such a move would finish them -- and they know it. (At least most of them do. I don't doubt there are some "true believers" among them, who will sooner or later be in for a rude awakening.)
So. No WAY are the puppet masters going to allow their puppets to force "big government" into a great big huge default. Their dirty little secret is that they need big government. But they need it to do THEIR bidding, not the bidding of US citizens. Which is why they invented the Tea Party in the first place.
Which is why the Republican leadership decided to rig the game in such a way that a simple yea or nay vote would never come up. It was a huge con and it looks like it's going to pay off big time. Obama has been hypnotized into believing he has to offer the Republicans something to get their cooperation and Boehner and Co. have been playing that for all it's worth. There's no reason for them to agree to raise taxes (and offend their base) when Obama's been signaling from the start that a default would be unacceptable and he'd do literally anything to avoid it.
The Republicans now smell blood and realize that if they hold out and continue to offer nothing in return for the draconian cuts Obama has already agreed to, then they can't lose. The debt limit will be raised AND Obama and the Democrats will be humiliated and reviled for caving in to unreasonable demands. If they were to make the mistake of actually compromising and agreeing to some tax hikes, then it might look like Obama was the winner. Why would they want to do that?
For the Dems the solution is obvious, but it would take some guts. Offer a very simple bill limited ONLY to the raising of the debt limit. Pass it in the Senate. And force the Tea Partiers in the House to decide whether they really want to take the heat for destroying the US economy AND the wealth of their patrons. Since no tax increase would be on the table, they needn't worry about violating their silly pledge. So all they'd be left with would be the argument that forcing the US into default is preferable to not cutting trillions out of Social Security, Medicare, education and Mom's Apple Pie. Is that a poker hand? I don't think so.