Negotiators are close to an agreement on a budget deal that would raise discretionary spending caps by upwards of $300 billion over two years and provide billions of dollars more for nondefense programs that are outside the constraints of the caps.

Republican and Democratic staff with knowledge of the talks said it’s possible but not assured a deal could be reached as early as today and attached to the House stopgap spending bill Wednesday or Thursday. The House spending package, introduced Monday night, is headed to the floor of that chamber for a vote Tuesday afternoon as an amendment to an unrelated bill.

“Even though a deal has eluded us for months, negotiators are now making significant progress. The Republican leader and I have been working together quite productively,” Senate Minority Leader Charles E. Schumer, D-N.Y., said on the floor. “We are closer to an agreement than we have ever been.”

If an agreement is reached on caps, it is also likely the Senate will attach a debt limit suspension to the stopgap. Any changes would then have to be approved by the House again, before the current continuing resolution expires after midnight Thursday.

As of this weekend, negotiators were considering raising the defense cap by $80 billion in fiscal 2018 and perhaps $85 billion in fiscal 2019, with the nondefense cap rising by $63 billion in 2018 and possibly more in 2019. Republicans were pressing to keep the nondefense cap at $63 billion in the second year, a person with knowledge of the talks said.

Though Democrats have insisted on parity or equal increases in the defense and nondefense caps, Democratic staff said they might be willing to accept smaller increases in the nondefense cap in return for new or higher funding for Democratic priorities that are funded on the mandatory side of the budget.

Adding new money for efforts to prevent opioids abuse, several more years of funding for community health centers, more funding for the Veterans Administration, a loan program to avoid cuts to multiemployer pension plans, disaster relief aid, and an agreement to provide security for immigrants who came to the United States illegally as children all have been under discussion as options to attach to a caps deal.

Unlike the past two cap-raising deals, negotiators have not been able to find a way to completely offset the discretionary spending increases in this one through cuts or changes to mandatory programs. A person with knowledge of the talks said less than 50 percent of the increase in discretionary spending would be offset.

It wasn’t immediately clear if House Democrats, or conservative House Republicans, would be on board with the emerging Senate agreement.

“The rumor is the Senate will put a caps agreement on that bill,” House Minority Whip Steny H. Hoyer said Tuesday morning.

If there is such an agreement it will likely include Senate and House priorities with both chamber’s minority leaders, Charles E. Schumer and Nancy Pelosi, involved in the negotiations, he said.

Nonetheless, Hoyer would not commit to House Democrats’ reaction.

“I’m going to wait to see what the Senate does before I say whether we’ll vote for or against,” he said.

“Well I hope we’re close, but we’ll see,” Pelosi said of a potential caps deal as she entered a Democratic cloakroom.

Jennifer Shutt, Kellie Mejdrich, Lindsey McPherson and Joe Williams contributed to this report.