Washington is preparing for a lengthy partial shutdown as a deal to fully reopen the government remains elusive.

Though only in its second day after Congress missed the midnight deadline Friday, lawmakers are warning they believe roughly a quarter of the government could remain shuttered well into the week.

Both Monday and Tuesday are federal holidays, but the ramifications of a partial shutdown are expected be felt more widely on Wednesday, the first federal workday since the missed deadline.

The Senate isn’t expected to formally reconvene until Thursday, and House lawmakers were told not to expect votes before then, raising the prospects that the partial closure could last for up to a week or longer.

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Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) disputed the notion that the schedule meant a deal was days off, saying he “didn’t take it as a sign of that.”

“Listen, anything can happen,” he said. “We’re pulling for an agreement that can get 60 votes in the Senate and a majority of votes in the House.”

But a McConnell aide predicted that without an agreement, the Thursday session could effectively turn into a brief pro forma, extending the amount of time senators are out of town.

While congressional leadership and the Trump administration are locked in negotiations about border funding — the major snag for the spending talks — there are no signs the White House and congressional Democrats are close to agreeing on a number that could pass both chambers and garner the president’s signature.

Incoming White House chief of staff Mick Mulvaney Mick MulvaneyOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security Blockchain trade group names Mick Mulvaney to board Mick Mulvaney to start hedge fund MORE told "Fox News Sunday" that it's "very possible this shutdown will go beyond the 28th and into the new Congress."

A senior administration official said the White House is standing by its demand for $5 billion in physical barriers and declined to “negotiate over the phone” when pressed on figures below the amount.

Trump is being encouraged by conservatives to dig in and “hang tough.” The president made the U.S.-Mexico border wall a key campaign promise and the issue, combined with hard-line immigration rhetoric, has found roots with his base.

Outgoing Rep. Pete Sessions Peter Anderson SessionsThe Hill's Campaign Report: New polls show Biden leading by landslide margins The Hill's Morning Report - Presented by Argentum - In Rose Garden, Trump launches anti-Biden screed Pete Sessions wins GOP runoff in comeback bid MORE (R-Texas), while predicting “cooler heads are prevailing,” also said the president shouldn’t accept below $5 billion for the border and encouraged him to use the bully pulpit to make his case.

“I honestly believe that we can and must get the wall,” Sessions said. “I think there should be a reality that the president also has an opportunity to speak to the American people in a way that they will understand it.”

But there are signs of shuttle diplomacy happening behind the scenes even if major hurdles remain between the White House and congressional Democrats. And both sides are floating trying to get a deal that would run through Sept. 30, the end of the fiscal year, rather than a stopgap measure into February.

Vice President Pence and Senate Minority Leader Charles Schumer Chuck SchumerCruz blocks amended resolution honoring Ginsburg over language about her dying wish Senate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' MORE (D-N.Y.) met on back-to-back days and exchanged offers. The White House is floating $2.1 billion for the border without restrictions on how the money can be spent, according to a source familiar with the negotiations.

Though still too high for Democrats, it’s less than half of the $5 billion figure the administration is advocating for publicly.

But conservatives argue that Democrats aren’t yet ready to come to the negotiating table, echoing Trump’s rhetoric that the minority is to blame for the partial shutdown of the GOP-controlled government.

“I do not believe that Sen. Schumer is serious about negotiating based on the conversations that I've heard and you know until he is serious about reaching a reasonable compromise it's not worth the time,“ said Rep. Mark Meadows Mark Randall MeadowsThe Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November House moves toward spending vote after bipartisan talks House Democrats mull delay on spending bill vote MORE (R-N.C.).

Schumer is reportedly asking for $1.3 billion for the border with restrictions on how the money is spent, in line with a number Democratic leadership has floated for weeks as they raced toward the shutdown deadline. Schumer, according a spokesman, was also using the meeting with Pence to reiterate that Democrats couldn’t support funding for a physical wall.

“Democrats have always been for smart and effective ways to secure our border,” Schumer said ahead of the meeting with Pence. “Every single proposal we made to the president included $1.3 billion for border security. The Trump shutdown provides zero dollars for border security.”

The back-and-forth are the latest turns in a days-long drama over funding roughly 25 percent of the government, including the Department of Homeland Security. An estimated 380,000 federal employees are being furloughed during the shutdown, while an estimated 420,000 employees will be required to work without pay.

The Senate initially passed a bill that would have funded that portion of the federal government through Feb. 8 and leadership predicted Trump would sign the bill. But House Republicans, with Trump’s blessing, added $5.7 billion for the border as well as disaster recovery money into the bill and kicked it back.

The GOP division is spilling over into the shutdown negotiations. Sources say Shelby urged the president to accept $1.6 billion, a figure Meadows told The Hill “is not going to work” for conservatives or the president.

Asked about the allegation, Shelby told The Hill that he urged the president to get the “best” deal and to remember that “come Jan. 3 the political equation changes.”

"I don't know. I think we're wanting more than that. Because that's $1.6 [billion] plus some other money and some other funds. Not just a single $1.6, it adds up to more,” Shelby added, asked if he thought $1.6 billion was the best deal Republicans would get.

Democrats, meanwhile, are feeling little pressure to cave to Trump’s wall demands after picking roughly 40 seats in the midterms and as they barrel toward Jan. 3, the day they take back the House's majority. They say if the shutdown is still continuing then, they’ll pass their preferred funding bill and kick it back to the House.

“If President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE and Republicans choose to continue this Trump Shutdown, the new House Democratic majority will swiftly pass legislation to re-open government in January,” Schumer and House Minority Leader Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE (D-Calif.) pledged in a joint statement shortly after the midnight deadline.

— Mile Lillis, Juliegrace Brufke and Melanie Zanona contributed to this report, which was updated at 9:31 a.m.