So now what? Now that Dems and Republicans have unveiled competing plans for the way forward — and now that both sides have dug in — what happens next?

Here’s the game plan, as seen by Senate Dem aides: The next move is to sit tight and wait for the House to vote on Boehner's proposal. The idea is that with mounting conservative opposition, it could very well be defeated. If the Boehner plan goes down in the House, that would represent a serious blow to Boehner’s leadership, weakening his hand in negotiations.

“The Senate will wait to act until we see if Speaker Boehner is able to pass a bill in the House,” a senior Senate Democratic aide says. “At the moment that’s an open question.”

It’s unclear as of yet where most Tea Partyers will come down on the Boehner proposal, but House conservatives are privately expressing serious reservation about the plan, arguing that it doesn’t cut spending enough, and the Republican Study Committee is dismissing Boehner’s plan as not “a real solution.” Dems hope that if conservatives do sink Boehner’s plan, it will reveal clearly that Boehner does need Democratic votes to get anything passed.

At that point, the Senate would then pass Harry Reid’s proposal, and then kick it over to the House, which would increase pressure on Boehner to try to get it passed, since he was unable to pass his own plan.

The second alternative possibility being gamed out by Senate Dems would take place if the Boehner plan does manage to sneak through the House. Aides say Dems would then vote it down in the Senate. And here’s where it gets even more interesting.

Senate Dem aides say they would then use Boehner’s bill — which passed the House but died in the Senate — to expedidate their own proposal. Here’s how. They would use the “shell” of the Boehner bill as a vehicle to pass Harry Reid’s proposal, because for various procedural reasons House messages get expedited consideration. Senate Dems would vote to “amend” Boehner’s bill by replacing it completely with Reid’s proposal — which the Senate could then pass more quickly than they otherwise could.

After that, Reid’s proposal — having passed the Senate — would then get kicked back to the House. Having proved that Boehner’s plan can’t pass the Senate, Democrats would in effect be giving House Republicans a choice: Either pass the Reid proposal, or take the blame for default and the economic calamity that ensues.

That’s the current Dem game plan, at any rate. And while the best laid plans often go astray — particularly in the alternate universe known as the United States Congress — the brinkmanship is only going to get even more intense over the next few days.

UPDATE: One other key point. The idea is that if the Boehner plan fails in the House, the pressure will increase on a few Senate Republicans to support Reid’s plan, making it possible to pass the Senate, because the alternative is default and Republicans will want to avoid blame for economic calamity. Keep in mind that Mitch McConnell has long said the debt ceiling must be raised, and has suggested the GOP must find a way for avoiding blame for failure to hike it.