Congress has been at loggerheads for months over how to raise the debt ceiling, barreling the United States closer to the brink of default.

Democrats have roundly rejected House Republicans' Limit, Save, Grow Act that passed last week to raise the debt limit in exchange for sweeping spending cuts. They want a clean debt ceiling extension bill without any conditions but have yet to be able to pass one in the Senate.

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While the future of how this will play out is uncertain, here are a few scenarios that could take place.

Breakthrough in Biden and McCarthy talks

President Joe Biden and House Speaker Kevin McCarthy (R-CA) haven't met since February. McCarthy has been adamant that any increase to the nation's borrowing authority be paired with spending cuts, a nonstarter with Democrats. Biden has repeatedly indicated that passage of a clean debt limit bill is nonnegotiable.

Still, the president offered to meet with McCarthy and other congressional leaders to discuss the crisis on May 9, when the House reconvenes, bending to fierce pressure from Republicans and even some Democrats to hold talks.

There are still ample dilemmas to overcome given the vast disparity in their positions. But perhaps as the threat of default grows near, the duo may be able to hash out a last-minute deal.

One side blinks

Both sides have dug their heels in very aggressively, and relenting would pose a political embarrassment. Failure could also doom McCarthy's fragile speakership. He barely clinched the gavel after a historic 15 rounds of voting, and hard-liners may not forgive a surrender to Biden.

Biden also doesn't want to be humiliated by Republicans heading into the 2024 cycle, nor does he want them to use the debt ceiling to leverage future concessions.

Given the dire ramifications of a default, however, one side may yield. Perhaps McCarthy could pass a clean bill with a pledge from Biden to do spending cuts shortly thereafter, or Biden could agree to smaller spending reductions than GOP's opening proposal.

Discharge petition

McCarthy has vowed not to put a clean debt ceiling bill on the floor, but some centrist members could bypass that with a discharge petition. With enough signatures, this maneuver could put a debt ceiling bill on the floor.

But there are a few hurdles in the way. First, the process is notoriously slow. A bill would have to be in committee for about a month, then likely need to amass 218 signatures to make it to the floor. From there, it must be on the House calendar for at least a week.

This is particularly dicey because Treasury Secretary Janet Yellen estimated in January that her department's "extraordinary measures" would last until at least June 5 and later gave an update Monday moving it up to June 1.

Other estimates vary. The Congressional Budget Office, for instance, previously projected in February that the funds will run dry between July and September. However, it recently moved that timetable up to early June.

If Congress winds up with more time to address the crisis, the discharge petition might become an option. So far, even Democrats don't appear particularly interested in using it.

One compromise framework floated by the bipartisan House Problem Solvers Caucus would cast the debt limit aside and then focus on budgeting reforms.

Deal with debt ceiling and government funding

Less commented on than the debt ceiling is the appropriations process. It is less urgent than default, but if neither side reaches an agreement by Sept. 30, there could be a government shutdown later this fall.

Dealing with the two issues simultaneously could remove the prospect of a future government shutdown and allow for some of the spending reforms McCarthy wants.

This is still tricky because it would technically require either McCarthy or Biden to ease up on their entrenched positions about either not raising the debt limit without cuts or negotiating over the nation's borrowing authority.

Additionally, appropriation negotiations are notoriously difficult to hash out and typically breed bipartisan agreements to increase spending.

Late last year, McCarthy was vexed by the Senate GOP's willingness to go along with a $1.7 trillion omnibus spending package. He wanted them to hold off until Republicans took over the House so they'd have more leverage. He quickly latched on to the debt ceiling as a way to address federal spending once he ascended to the speakership.

US defaults

One thing that all sides agree on is that a default would be economically ruinous. The precise repercussions are a bit unknown.

In 2011, Standard & Poor's downgraded the nation's high-tier AAA rating to its current AA+ rating just days after Congress passed a bill to raise the debt ceiling. The move came in the background of grumblings about the budget on the hill.

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An actual default could see the U.S. credit rating slip much more dramatically and spike interest payments on its debt interest obligations.

One projection cited by RSM International in March found that a technical default could boost unemployment to 7%, and an actual one could rocket unemployment to 12% while causing over a 10% economic contraction and massive inflation.