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The big story in Washington Monday was about lively efforts to strike a budget-and-debt deal to stave off a potential fiscal crisis. But the names in the headlines were President Obama and senators like Harry Reid, Mitch McConnell, and John McCain.

That raises an important question: With time ticking down toward an Oct. 17 deadline, will House Republicans including tea party enthusiasts climb aboard to help a deal happen?

If not, it could be a bumpy ride ahead for financial markets and the political system.

After all, for a 鈥渄eal鈥� to really work 鈥� to actually reach Mr. Obama鈥檚 desk for a signature 鈥� it needs to be approved by the Republican-controlled House as well as the Senate. There are essentially three paths forward for the House.

Path 1: compromise. In this scenario, most Republicans vote to support a bargain that raises the debt limit and funds the government, even though the plan may not include the kind of concessions from Democrats that they鈥檇 like.

Path 2: let Democrats pass it. In theory, Speaker John Boehner (R) of Ohio could allow a bill to pass, even if most Republicans don't support it. There are 200 Democrats in the chamber, and only 217 votes are needed for a bill to pass, so Democrats would need only 17 Republican defectors. Mr. Boehner has said he鈥檚 opposed to letting the country go over a debt-limit cliff on Oct. 17 and default on Treasury obligations. But this scenario would mean breaking the so-called Hastert rule 鈥� the notion that a speaker should not bring a bill to the floor for a vote unless a majority of his caucus supports it. If Boehner goes this route and faces the wrath of a restive tea party wing, it could cost him his speakership.

Path 3: failure. This happens if the House rejects the Senate deal or makes changes that would require negotiations past Oct. 17. That wouldn鈥檛 necessarily mean the US fails to make payments due on its debt. (The Treasury might have wiggle room to avoid an official default.) But if Congress didn鈥檛 fix the mess by quickly reaching a successful House-Senate deal, the Treasury would soon be unable to pay all federal obligations.

That last scenario would have serious consequences, scaring stock market investors and putting brakes on economic growth, forecasters say.

Which path will it be for the House?

At this point, it鈥檚 hard to rule any of the three scenarios out. House Republicans have an incentive to avoid a mid-October breach of the debt limit, in which polls suggest they would bear the brunt of public blame. And Boehner has an incentive to try to get a deal that a majority of his caucus can support.

But in public comments, House Republicans don't sound eager to just rubber-stamp a boost in the nation's borrowing limit and a "continuing resolution" to fund the government and end the shutdown.

鈥淲e have got to deal with our deficit spending and ultimately our debt,鈥� Rep. Diane Black (R) of Tennessee said on CNN Sunday. 鈥淭hat means structural changes to our entitlement programs. And so I really need to make sure that that's a part of [a deal], because we cannot continue to spend the way we are.鈥�

Many Republicans agree that raising the debt ceiling to allow more borrowing should only be done with some new spending restraint attached.

Rep. Jim Jordan (R) of Ohio, on Fox News Sunday, said two principles continue to propel many in his party.

鈥淲e can't keep raising the limit on an already maxed out credit cart,鈥� he said. 鈥淭he second principle is this: Obamacare, the way it's being implemented, is unfair.鈥�

That explains why Republicans in the House have urged their Senate colleagues to stand firm to win something significant from Democrats in this week鈥檚 fiscal bargaining.

Other House Republicans 鈥� notably ones who don鈥檛 come from politically 鈥渟afe鈥� conservative districts 鈥� are looking for a face-saving way out of the standoff over raising the debt cap and ending a partial government shutdown.

Senate negotiators from both parties cited progress in talks on Monday. But Obama had to shift a scheduled meeting with congressional leaders from Monday afternoon to Tuesday, to give bargainers more time.

They can鈥檛 take too long, however, with that Oct. 17 deadline drawing near.