Experts in Washington and on Wall Street are making their best guesses for how close the government will come to defaulting in the months ahead if Congress remains gridlocked.

A key date that keeps coming up is June 15.

That is the deadline for taxpayers to pay their second installment of estimated taxes for 2023. It's also likely the next time the government’s books will improve appreciably now that the main tax season is winding down.

Those funds — combined with financial flexibility offered by accounting maneuvers the Treasury Department can deploy — are what stands between the US and a default.

What's likely to happen between now and then is that Treasury “will gradually burn through its remaining cash on hand and extraordinary measures” to pay for government operations, Shai Akabas of the Bipartisan Policy Center told Yahoo Finance by email.

Balances that could get 'dangerously low’

As of April 19, the Treasury Department’s general account had a closing balance of about $265.1 billion. Its balance sheet is expected to improve for a few more days as more tax returns are processed before beginning a gradual decline.

The question is how low the balance will go.

Without a deal in Congress, "it’s possible that Treasury’s cash on hand will be dangerously low in early June prior to an influx of quarterly revenues mid-month," Akabas wrote.

Wrightson ICAP, a research firm that specializes in economic data, projects that Treasury's operating balance could fall to a low of $26 billion on June 8 before temporarily turning around as quarterly taxes come in.

A projected balance like that may be enough to avoid a default in June, but the uncertainty inherent in making these projections means no one yet can rule out a balance of $0 that month.

Wrightson currently predicts a 20% chance of a June X-date, but experts there and elsewhere emphasize that it won't be until May — when final tax season revenue data is in — to definitively say one way or another.