WASHINGTON — The Senate gave final approval late Thursday to a debt ceiling and budget cuts package, grinding into the night to wrap up work on the bipartisan deal and send it to President Biden’s desk to become law before a fast-approaching deadline that threatened a federal default.

The compromise package negotiated between Mr. Biden and Speaker McCarthy leaves neither Republicans nor Democrats fully pleased with the outcome. But the result, after weeks of hard-fought budget negotiations, shelves the volatile debt ceiling issue that risked upending the  economy until 2025 after the next presidential election.

Approval in the Senate on a bipartisan vote, 63-36, somewhat reflected the overwhelming House tally the day before, relying on centrists in both parties to pull the Biden-McCarthy package to passage — though Democrats led the tally in both chambers.

Senator Schumer said ahead of voting that the bill’s passage means “America can breathe a sigh of relief.”

Afterward he said, “We’ve saved the country from the scourge of default.”

Mr. Biden said in a statement following passage that senators from both parties “demonstrated once more that America is a nation that pays its bills and meets its obligations — and always will be.”

He said he would sign the bill into law as soon as possible. “No one gets everything they want in a negotiation, but make no mistake: this bipartisan agreement is a big win for our economy and the American people,” the president said. The White House said he would address the nation about the matter at 7 p.m. Eastern time on Friday.

Fast action was vital if Washington hoped to meet the June 5 deadline, when Treasury has said America would start running short of cash to pay its bills. Raising the nation’s debt limit, now $31.4 trillion, would ensure Treasury could borrow to pay already incurred debts and other obligations.

In the end, the debt ceiling showdown was a familiar high-stakes battle in Congress, a fight taken on by McCarthy and powered by a hard-right House Republican majority confronting the Democratic president with a new era of divided government in Washington.

Refusing a once routine vote to allow a the nation’s debt limit to be lifted without concessions, Mr. McCarthy brought Mr. Biden’s White House to the negotiating table to strike an agreement that forces spending cutbacks aimed at curbing the nation’s deficits.

Overall, the 99-page bill restricts spending for the next two years, suspends the debt ceiling into January 2025 and changes some policies, including imposing new work requirements for older Americans receiving food aid and greenlighting an Appalachian natural gas line that many Democrats oppose.

It bolsters funds for defense and veterans, cuts back new money for Internal Revenue Service agents and rejects Mr. Biden’s call to roll back Trump-era tax breaks to help cover the nation’s deficits. It imposes automatic 1 percent cuts if Congress fails approve its annual spending bills.

After the House overwhelmingly approved the package late Wednesday, Senator McConnell signaled he too wanted to waste no time ensuring it became law.

Touting its budget cuts, Mr. McConnell said Thursday, “The Senate has a chance to make that important progress a reality.”

Having remained largely on the sidelines during much of the Biden-McCarthy negotiations, several senators insisted on debate over their ideas to reshape the package. But making any changes at this stage would almost certainly derail the compromise and none were approved.

Instead, senators dragged through rounds of voting late into the night rejecting the various amendments, but making their preferences clear. Some Republican senators wanted to include further cut spending, while Senator Kaine of Virginia sought to remove the Mountain Valley Pipeline approval.

The energy pipeline is important to Senator Manchin of West Virginia and he defended the development running through his state, saying the country cannot run without the power of gas, coal, wind and all available energy sources.

But, offering an amendment to strip the pipeline from the package, Mr. Kaine argued it would not be fair for Congress to step into a controversial project that he said would also course through his state and scoop up lands in Appalachia that have been in families for generations.

Defense hawks led by Senator Graham of South Carolina complained strongly that military spending, though boosted in the deal, was not enough to keep pace with inflation — particularly as they eye supplemental spending that will be needed this summer to support Ukraine against the war waged by President Putin.

“Putin’s invasion is a defining moment of the 21st century,” Mr. Graham argued from the Senate floor. “What the House did is wrong.”

They secured an agreement from Schumer, which he read on the floor, stating that the debt ceiling deal “does nothing” to limit the Senate’s ability to approve other emergency supplemental funds for national security, including for Ukraine, or for disaster relief and other issues of national importance.

All told, most of the Democratic senators voted for the package, while most of the Republicans opposed it. The tally was 46 Democrats and 17 Republicans in favor; 31 Republicans along with four Democrats and one independent who caucuses with the Democrats opposed.

In the House, too, Democrats ensured passage on a robust 314-117 vote. All told, 71 House Republicans broke with McCarthy to reject the deal.