Senate leaders on Tuesday said they are close to a two-year budget deal that could avert a government shutdown and set up a debate on immigration reform next week.

The deal would set spending levels for fiscal 2018 and 2019 and avoid the prospect of a second government shutdown Thursday when a stopgap spending measure expires.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) and Democratic Leader Charles Schumer Chuck SchumerMcConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt Schumer lashes out at Trump over 'blue states' remark: 'What a disgrace' MORE (N.Y.) touted their progress after meeting in McConnell’s office Tuesday morning.

“I’m optimistic that very soon we’ll be able to reach an agreement,” McConnell told reporters, predicting that another shutdown this week is very unlikely.

“I don’t think that’s going to happen,” McConnell said of a possible shutdown. “I think we’re on the way to getting an agreement and on the way to getting an agreement very soon.”

Schumer said he also expected a deal soon that would set higher spending levels for defense and nondefense programs.

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“I’m very pleased to report my meeting with Leader McConnell went very well. We’re making real progress on a spending deal that would increase the caps for both military and middle-class priorities on the domestic side that my colleagues have been fighting for.”

Schumer said some “outstanding issues” remain, but stressed he is “very hopeful” for a deal.

One issue could be House Democrats.

Schumer won’t sign off on a final deal unless Minority Leader Nancy Pelosi Nancy PelosiMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Pelosi must go — the House is in dire need of new leadership MORE (D-Calif.) supports it, and the legislation will need the backing of House Democrats to get through that chamber, according to Democratic aides.

Pelosi is under pressure from members of her caucus to get a commitment from Speaker Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.) on a House vote to protect immigrants brought to the United States as children who could face deportation beginning next month.

In the Senate, McConnell has agreed to a floor debate meant to produce immigration legislation.

Rep. Luis Gutiérrez (D-Ill.) said these immigrants should not be left to the side and expressed anger they are not included in the initial deal being reported.

“Do you really think we’d be having this dialogue if every Planned Parenthood office were to come to a halt — I mean, shuttered. I don’t think so,” he said. “I think, however, unfortunately, it’s OK to do it to ‘Dreamers.’ It’s OK to turn your back and walk away from Dreamers. And I think that’s unfortunate.”

Under the proposed deal, the Senate would approve as early as Wednesday a stopgap measure to keep the government open for six weeks. The legislation would also include budgetary ceilings for defense and nondefense spending that reflect the Schumer-McConnell agreement.

Defense spending would be raised more than nondefense spending, breaking the dollar-for-dollar link that Democrats have insisted upon. Lawmakers said the defense spending budget cap for 2018 likely would be hiked by $80 billion, while the nondefense cap would be hiked by $63 billion.

While this would be a concession from Democrats, they agreed to a deal last spring that broke the dollar-for-dollar link. And Democrats could also get money for community health centers and disaster relief as part of the stopgap, though some of those details are still under negotiation.

The stopgap would give Congress more time to work on the longer-term omnibus funding bill, which would cover government spending for the rest of fiscal 2018.

The optimistic takes from Schumer and McConnell stood in contrast to remarks from President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE on Tuesday, who said he welcomed a shutdown if it would get Democrats to bend.

“I’d love to see a shutdown if we don’t get this stuff taken care of,” Trump said at a White House meeting.

“If we have to shut it down because the Democrats don’t want safety and, unrelated but still related, they don’t want to take care of our military, then shut it down.”

Trump’s statement angered Schumer, but didn’t appear to put the potential agreement in any danger.

“That speaks for itself. We had one Trump shutdown, nobody wants another, maybe except him,” Schumer said.

It appears lawmakers in both parties would rather avoid more shutdowns after the three-day government stoppage in January. While Democrats were seen as getting the worst of that one , both parties are tired of the stopgap funding measures and see risks in the perpetual shutdowns.

One Republican lawmaker attending the White House meeting pushed back at Trump.

“We don’t need a government shutdown on this,” Rep. Barbara Comstock Barbara Jean ComstockLive coverage: House holds third day of public impeachment hearings Gun debate raises stakes in battle for Virginia legislature Progressives face steep odds in ousting incumbent Democrats MORE (Va.) said, according to a White House pool report. Comstock represents constituents in a Virginia suburb of Washington, D.C., that includes thousands of federal workers. She’s also a top Democratic target in the midterm elections.

The House on Tuesday approved a six-week stopgap in a 245-182 vote that also includes a year of defense spending.

The current plan is for the Senate to vote on a stand-alone, yearlong defense appropriations bill as soon as Wednesday. If leaders can’t get unanimous consent to speed up proceedings, the vote would happen Thursday, however.

That vote will almost certainly fail to reach the 60 votes necessary to end a filibuster, and is intended to demonstrate that the House bill does not have enough votes to pass the Senate, according to a senior Senate aide familiar with internal deliberations.

If Democrats block a bill, McConnell could then amend the House resolution to include the budget caps.

In the House, the deal seems likely to draw opposition from conservative Republicans, though members of the House Freedom Caucus said they needed to review details before taking a position.

“It depends on what the budget caps deal is. Some of the numbers that are being talked about are obviously much higher than what conservatives would support,” Freedom Caucus Chairman Mark Meadows Mark Randall MeadowsTrump won't attend UN General Assembly in person, Meadows says McConnell focuses on confirming judicial nominees with COVID-19 talks stalled Overnight Health Care: Ex-Pence aide backs Biden over virus response | Trump's sharp words put CDC director on hot seat | Trump coronavirus adviser threatens to sue Stanford researchers MORE (R-N.C.) told The Hill on Tuesday afternoon.

“We’ll have to look. I want to see what comes back. Are they going to put the disaster money on this? Are they going to put debt ceiling on this?” said Rep. Jim Jordan James (Jim) Daniel JordanHouse passes resolution condemning anti-Asian discrimination relating to coronavirus Republicans call for Judiciary hearing into unrest in cities run by Democrats Trump, GOP seek to rebut Democratic narrative on night one MORE (R-Ohio), a former chairman of the Freedom Caucus. “I’m for increasing defense, but then holding the line on nondefense.”

Congress also needs to raise the debt ceiling soon, in part because the federal government is taking in less tax revenue after the passage of December’s tax-cut package.

Jordan argued that pairing an $81 billion disaster aid package with higher spending caps would amount to “the second-largest discretionary spending increase in a decade.”

“That would be problematic for me,” he added.

Ryan could tweak the Senate bill to make it more acceptable to conservatives and send it back to the Senate, but that would be risky with government funding due to expire on Feb. 8.

Though some House Democrats may oppose a bill without commitments on immigration, a large number are likely to support any deal that their leaders sign off on, especially if it includes increases for domestic programs, funding for community health centers and other Democratic priorities.

“We’ll have to see it, but we’re looking for a CR that provides for a resolution of our budget issues. And that means caps that get us off of the sequestration level,” said Rep. David Price David Eugene PriceHouse panel approves measure requiring masks on public transport Overnight Energy: 350 facilities skip reporting water pollution | Panel votes to block Trump's 'secret science' rule | Court upholds regulation boosting electric grid storage Committee votes to block Trump's 'secret science' EPA rule MORE (D-N.C.), an appropriator.

Jordain Carney, Mike Lillis and Scott Wong contributed.