Senate Minority Leader Mitch McConnell (R-Ky.) told reporters yesterday, “There will not be a government shutdown.” His confidence was reassuring, but it’s not at all clear he’s correct.

Republicans and Democrats plunged into another round of brinksmanship on Tuesday as a fight over disaster aid brought the renewed threat of a government shutdown.

With the House prepared to vote on a bill to keep the government running past Sept. 30, when current funding expires, Senate Majority Leader Harry Reid (D-Nev.) said the upper chamber would send the bill back if House Republicans did not increase money for the Federal Emergency Management Agency (FEMA).

Reid warned that the government could shutter at the end of the month if the dispute was not resolved. “We are not going to cave on this,” he told reporters Tuesday afternoon.

This, predictably, led to a new round of House Republican leaders blaming Senate Democratic leaders for not going along with the GOP’s plan, insisting that Reid should get the blame if there’s a shutdown.

Disaster relief funding continues to be at the heart of the dispute. The Senate approved resources for FEMA and treated the funding the way Congress always has: as an emergency, without offsets. The House GOP wants fewer resources for FEMA, and says relief must come with strings attached: offsets that include cuts to a job-creating clean-energy program the right doesn’t like.

House Republican leaders insist they won’t even consider the Senate’s FEMA measure — indeed, they say the votes for passing it simply won’t materialize — while Reid, perhaps concerned about setting a new precedent regarding disaster aid, is vowing to stand firm.

The deadline is Sept. 30, which is a week from Friday. Congress is supposed to be out next week, which may complicate the process.

I’m not prepared to make any predictions just yet, but I’ll just say this: Congress has a 12% approval rating. The institution has never been popular, but the legislative branch of government hasn’t seen public disgust this intense since the dawn of modern polling.

If Republicans shut down the government because they don’t want to fund disaster relief without cuts, public revulsion is bound to get significantly worse.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.