Markets and investors will be watching keenly for even a glimmer of hope that leaders are looking towards a path out of the debt-ceiling crisis when President Joe Biden sits down with House Speaker Kevin McCarthy later today.

The meeting comes as economic pressure increases following Treasury Secretary Janet Yellen's announcement that the US could default as early as June 1.

A wave of recent independent projections confirmed that a market-rattling default could be just weeks away, including a new analysis from the Bipartisan Policy Center released Tuesday morning that finds growing risk of a default in early June.

"Treasury is skating on very thin ice in June," notes Shai Akabas, the group's director of economic policy.

Today's high-stakes Oval Office gathering begins at 4 pm ET, with House Democratic Leader Hakeem Jeffries (D-NY), Senate Majority Leader Chuck Schumer (D-NY), and Senate Minority Leader Mitch McConnell (R-KY) also in attendance.

Optimism isn’t high, with both parties increasingly dug into irreconcilable positions and experts predicting that markets could turn volatile within weeks as the "X-date" approaches.

Mike Konczal, a director at the Roosevelt Institute, added a warning Monday that people shouldn’t assume the crisis can be resolved at the last minute like lawmakers did in 2011, citing the much thinner margin that Speaker McCarthy enjoys now compared to his predecessors.

He says lawmakers shouldn't “come away thinking the financial markets will necessarily come in at the last minute and scare everyone into taking this seriously.”

Here are 5 signs to watch that could signal a path forward—or further extinguish hopes that bipartisan compromise is possible in the weeks ahead.

1) Do the White House or McCarthy signal any flexibility?

The key question, of course, is whether Democrats or Republicans offer any flexibility from their entrenched positions.

Biden and McCarthy have been talking past each other for months now. Democrats say that the debt ceiling is simply too dangerous to be a bargaining chip; their position is that it therefore needs to be raised without pre-conditions before a debt conversation can take place in the fall around annual budget talks.

Republicans have shot back that a so-called “clean” increase is off the table; they passed a plan in April that repealed large swaths of Biden’s accomplishments in exchange for an increase.

Both sides have become even more entrenched in recent days.

Biden ally Jeffries said on NBC Sunday that a clean increase was “the only responsible thing to do” while a key McCarthy ally, Rep. Patrick McHenry (R-NC), reiterated on CBS that “President Biden has to come to the table for a negotiated solution.”

One early signal the meeting is unlikely to yield quick results is where Biden plans to travel next. He has already announced he’ll follow up Tuesday’s meeting with a trip Wednesday to New York's Hudson River Valley for a speech on the debt limit in the district of Rep. Mike Lawler (R-NY), a vulnerable Republican under pressure to break from his party.

2) Is a short-term extension discussed?

Another way to avoid default would be to pass a bill to delay the conversation for at least a few months.

Treasury Secretary Janet Yellen said in an ABC interview on Sunday that Biden “wants to set up a process in which spending priorities and levels are discussed” down the road, likely in the fall.

Other Biden officials have noted that a short-term extension will be on the table, with the question being whether Republicans will be amenable to delaying a showdown and merging debt-ceiling conversations with larger budget conversations.

Hours before the meeting, Speaker McCarthy told reporters that he opposes the idea of a short term extension through Sept. 30 but there is historic precedent for moves to line up the two issues.

The 2013 debt ceiling crisis ended first with a short term deal that required each chamber to pass a budget and then later in the year set up conferences to reconcile budgets as part of a broader agreement that also took default off the table.

3) Is anyone talking about areas of agreement afterwards?

In spite of all the partisan rhetoric, there are areas where Democrats and Republicans potentially could find agreement in the weeks ahead.

One example is the subject of deficit reduction, a principle the two sides have in common. The GOP bill would cut deficits by $4.8 trillion over 10 years while President Biden has already proposed a budget that includes about $3 trillion in deficit reduction. Both sides largely disagree where to make those cuts but are on the record as being in favor of such cuts generally.

Another example could be on energy policy. The Republican debt ceiling bill included a suite of energy reforms. While some provisions are nonstarters at the White House, reforms to speed up the process of getting energy projects off the ground has been a bipartisan priority over the years.

Sen. Joe Manchin (D-WV) made a run at the issue last year. While that effort ultimately fell short, Manchin will be discussing it further this week.

If the two sides bring up these issues during Tuesday’s gathering, it could be a sign that they are at least beginning to imagine the shape of a possible deal.

4) Does Mitch McConnell continue to stay out of it?

Another key question is whether any daylight opens up between McCarthy and his GOP counterpart at the negotiating table. The Speaker’s bargaining position has been considerably strengthened by Senate Republicans putting up a unified front and saying that McCarthy is the party’s sole representative on the issue.

McConnell himself has repeatedly deferred on the issue, saying recently that “the White House needs to stop wasting time and start negotiating with the Speaker of the House.”

There are few signs McConnell will change tack anytime soon. Just this weekend, a group of 43 Senate Republicans signed onto a letter stating that they won’t vote for a deal that doesn’t include “substantive spending and budget reforms.” McConnell and his entire leadership team co-signed that effort.

As for what she expects Tuesday, Sen. Joni Ernst (R-IA) told Politico she expects McConnell to say little Tuesday beyond “I’m here to support McCarthy.”

5) Do Democrats openly discuss end-runs around McCarthy?

A final question is whether Biden and his aides sound more open to some of the far-out fixes to the debt ceiling crisis.

One possibility is the 14th Amendment to the Constitution. The Civil-War era amendment includes a line that "the public debt of the United States, authorized by law...shall not be questioned." Advocates say it can be invoked as a pretext to simply announce that the government will continue to borrow.

But Biden, when asked about the chances of invoking the 14th Amendment last week in an MSNBC interview, said "I've not gotten there yet," with Yellen adding Sunday on ABC that the option could lead to a "constitutional crisis."

A second option is a long-shot maneuver called a discharge petition which could allow Democrats to team up with moderate Republicans to force a House vote over McCarthy’s objections. Jeffries and other House Democrats announced that an effort is already underway on that front.

If Biden or other Democrats begin talking more openly about those options, it may be a sign that talks are further breaking down.

This post has been updated.

Ben Werschkul is Washington correspondent for Yahoo Finance.

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