WASHINGTON — President Biden says he “feels good” about the debt ceiling and budget deal negotiated with Speaker McCarthy as the White House and congressional leaders work to ensure its passage this week in time to lift the nation’s borrowing limit and prevent a default.

Mr. Biden spent part of the Memorial Day holiday working the phones, calling lawmakers in both parties, as the president does his part to deliver the votes. A number of conservatives are criticizing the deal as falling short of the deep spending cuts they wanted, while liberals decry policy changes such as new work requirements for older Americans in the food aid program.

A key test will come Tuesday afternoon when the House Rules Committee is scheduled to consider the package and vote on sending it to the full House for a vote expected Wednesday.

“I feel very good about it,” Mr. Biden told reporters Monday as he left Washington for his home in Delaware.

“I’ve spoken to a number of the members,” he said, among them Senator McConnell, a past partner in big bipartisan deals who largely sat this one out.

“I spoke to a whole bunch of people, and it feels good,” Mr. Biden said.

To those progressive Democrats raising concerns about the package, the president had a simple message: “Talk to me.”

As lawmakers size up the 99-page bill, few are expected to be fully satisfied with the final product. But Mr. Biden, a Democrat, and Mr. McCarthy, a Republican, are counting on pulling majority support from the political center, a rarity in divided Washington, to join in voting to prevent a catastrophic federal default.

Wall Street will open Tuesday morning delivering its own assessment, as the financial markets that had been closed when the deal was struck over the weekend show their reaction to the outcome.

Mr. McCarthy acknowledged the hard-fought compromise with Mr. Biden will not be “100 percent of what everybody wants” as he leads a slim House majority powered by hard-right conservatives.

Facing potential blowback from his conservative ranks, the Republican speaker will have to rely on upwards of half the House Democrats and half the House Republicans to push the debt ceiling package to passage.

Overall, the package is a tradeoff that would impose some spending reductions for the next two years along with a suspension of the debt limit into January 2025, pushing the volatile political issue past the next presidential election. Raising the debt limit, now $31 trillion, would allow Treasury to continue borrowing to pay the nation’s already incurred bills.

Additionally, policy issues are raising the most objections from lawmakers.

Liberal lawmakers fought hard but were unable to stop new work requirements for people 50 to 54 who receive government food assistance and are otherwise able-bodied without dependents. 

The Republicans demanded the bolstered work requirements as part of the deal, but some say the changes to the food stamp program are not enough.

The Republicans were also pushing to beef up work requirements for health care and other aid; Mr. Biden refused to go along on those.

Questions are also being raised about an unexpected provision that essentially gives congressional approval to the Mountain Valley Pipeline, a natural gas project important to Senator Manchin, that many Democrats and others oppose.

At the same time, conservative Republicans including those from the House Freedom Caucus say the budget slashing does not go nearly far enough to have their support.

“No one claiming to be a conservative could justify a YES vote,” tweeted Congressman Bob Good.

This “deal” is insanity,” said Congressman Ralph Norman. “Not gonna vote to bankrupt our country.”

All told the package would hold spending essentially flat for the coming year, while allowing increases for military and veterans accounts. It would cap growth at 1 percent for 2025.

The House Rules Committee has three members from the influential Freedom Caucus who may very well try to block the package from advancing, forcing Mr. McCarthy to rely on the Democrats on the panel to ensure the bill can be sent to the House floor.

The House aims to vote Wednesday and send the bill to the Senate, where Mr. Schumer along with Mr. McConnell are working for a quick passage by week’s end.

Senators, who have remained largely on the sidelines during much of the negotiations between the president and the House speaker, began inserting themselves more forcefully into the debate.

Some senators are insisting on amendments to reshape the package from both the left and right flanks. That could require time-consuming debates that delay final approval of the deal.

Senator Kaine of Virginia is “extremely disappointed” by the provision greenlighting the controversial Mountain Valley Pipeline, his office said in a statement. He plans to file an amendment to remove the provision from the package.

Senator Graham of South Carolina complained that the military spending increases are not enough. “I will use all powers available to me in the Senate to have amendment votes to undo this catastrophe for defense,” he tweeted.

Yet making any changes to the package at this stage seems highly unlikely with so little time to spare. Congress and the White House are racing to meet the Monday deadline now less than a week away. 

That’s when Treasury Secretary Yellen has said the U.S. would run short of cash and face an unprecedented debt default without action.

A default would almost certainly crush the U.S. economy and spill over around the globe, as the world’s reliance on the stability of the American dollar and the country’s leadership fall into question.