Senate leaders hope to approve a budget deal Thursday to keep the government operating past midnight amid opposition from Democratic liberals and tea-party Republicans. 

The bipartisan compromise would provide the Pentagon and domestic programs with an extra $300 billion over the next two years. That additional spending worries some deficit-minded Republicans, and some Democrats are unhappy that immigration isn't part of the measure.

To that end, House Democratic leader Nancy Pelosi staged a record eight-hour speech arguing in favor of legislation for young immigrants in the country since childhood who face deportation.

The White House backs the Senate deal. Senate leaders hope to approve the measure Thursday and send it to the House for approval. But hurdles remain to avert the second shutdown in a month.

White House press secretary Sarah Huckabee Sanders says the deal will provide "certainty" for the next two years and achieves a "much needed" increase in funding for the national defense. The deal was also praised by Defense Secretary Jim Mattis.

Sanders says it will move the White House away from "crisis to crisis budgeting."

Senate Majority Leader Mitch McConnell said the measure would rewrite existing defense limits that have "hamstrung our armed forces and jeopardized our national security."

The measure, aides said, also contains almost $90 billion in overdue disaster aid and an increase in the government borrowing cap that would prevent a first-ever U.S. government default on its obligations.

Senate Minority Leader Chuck Schumer celebrated the new budget agreement but made little mention about what isn't coming with the new two-year agreement - a plan to protect the "Dreamer" immigrants.

The Democratic leader has dropped his push to use the budget talks to extract concessions on immigration from Republicans, leaving aside threats to shut down the government over the issue.

In remarks on the Senate floor, Schumer focused on the new agreement as a rare moment of bipartisanship and cooperation. He called it "the best thing we've done" for the middle class and the economy.

"We have reached the budget deal that neither side loves but both sides can be proud of," Schumer said.

On Tuesday, the House voted to pass a short-term government spending bill that would also provide new funding to the military through September. The bill's funding for the rest of the government would expire next month. 

The vote was 245-182. House GOP appropriators unveiled the short-term spending bill, known as continuing resolution (CR), that would also fund the military at increased levels through the rest of the fiscal year, which ends Sept. 30. The rest of the government would operate under 2017-level funding through March 23. GOP leaders pitched the plan to rank-and-file Republicans Monday evening at a closed-door meeting.

The measure would not provide a fix for undocumented immigrants brought to the U.S. as children. Nor would it increase border security or provide funding for a southern border wall.

But the plan would still have to make its way through the Senate, where its future is less certain. 

Negotiators are scrambling to strike a deal as the clock ticks toward the Thursday night deadline to keep the government funded. A budget agreement would almost certainly mean that many Democrats would support it, thereby guaranteeing that there wouldn't be another shutdown.

"I don't think that's going to happen," McConnell said about the prospects of a shutdown.

Meanwhile, President Trump said Tuesday afternoon at a White House roundtable on MS-13 gang violence, "I'd love to see a shutdown if we don't see this taken care of." Last year, Trump said that the country could use a "good shutdown."

Asked to respond to this comment Tuesday, Schumer said, "Speaks for itself. We had one Trump shutdown, nobody wants another maybe except him."

CBS News' Alan He and Katiana Krawchenko contributed to this report.

(The Associated Press, CBS News contributed to this report.)