Senate Republicans voting in a dramatic late Saturday session narrowly cleared a key procedural step as they race to advance President Trump’s package of tax breaks, spending cuts and bolstered deportation funds by his July Fourth deadline.

The tally, 51-49, came after a tumultuous night with Vice President Vance at the Capitol to break a potential tie. Tense scenes played out in the chamber as voting came to a standstill, dragging for more than three hours as holdout senators huddled for negotiations, and took private meetings off the floor. In the end, two Republicans opposed the motion to proceed, joining all Democrats.

There’s still a long weekend of work to come. Saturday’s procedural vote tees up a final Senate vote on the bill that will likely happen sometime Sunday or Monday, after which the measure returns to the House for passage there before hitting Mr. Trump’s desk at the White House.

Mr. Trump lashed out against holdouts before the vote, threatening to campaign against one Republican, Senator Tillis, who said he could not support the bill because of grave Medicaid cuts that he worried would leave many without health care in his state. Mr. Tillis and Senator Paul voted against.

Additionally, a provision would increase the nation’s debt limit, by $5 trillion, to allow continued borrowing to pay already accrued bills. Altogether, keeping the existing tax breaks and adding the new ones is expected to cost $3.8 trillion over the decade, the CBO says in its analysis of the House bill. An analysis of the Senate draft said it would add $3.9 trillion over the same period.

Pressure was mounting from all sides — billionaire Elon Musk criticized the package as “utterly insane and destructive.”

“The latest Senate draft bill will destroy millions of jobs in America and cause immense strategic harm to our country,” Mr. Musk wrote on X on Saturday. “It gives handouts to industries of the past while severely damaging industries of the future.”

The Tesla and SpaceX CEO later posted that the bill would be “political suicide for the Republican Party.”

The 940-page “One Big Beautiful Bill Act was released shortly before midnight Friday, and senators are expected to grind through all-night debate and amendments in the days ahead. If the Senate is able to pass it, the bill would go back to the House for a final round of votes before it could reach the White House.

With the narrow Republican majorities in the House and Senate, leaders need almost every lawmaker on board. A new analysis from the nonpartisan Congressional Budget Office said the Senate bill would increase by 11.8 million the number of people without health insurance in 2034.

At its core, the legislation would make permanent many of the tax breaks from Mr. Trump’s first term that would otherwise expire by year’s end if Congress fails to act, resulting in a potential tax increase on Americans. The bill would add new breaks, including no taxes on tips or overtime, and commit $350 billion to Mr. Trump’s mass deportation agenda.

But the cutbacks to Medicaid, food stamps and green energy investments, which a top Democrat, Senator Wyden, said would be a “death sentence” for America’s wind and solar industries, are also causing dissent within GOP ranks.

The final text includes a proposal for cuts to the Medicaid provider tax that had run into parliamentary hurdles and objections from several senators worried about the fate of rural hospitals. The new version extends the start date for those cuts and establishes a $25 billion fund to aid rural hospitals and providers.

The CBO had said that under the House-passed version of the bill, some 10.9 million more people would go without health care and at least 3 million fewer would qualify for food aid. The budget office has started releasing initial assessments of the Senate draft, which proposes steeper reductions.

Top income-earners would see about a $12,000 tax cut under the House bill, while the package would cost the poorest Americans $1,600, the CBO said.

The Senate included a compromise over the so-called SALT provision, a deduction for state and local taxes that has been a top priority of lawmakers from New York and other high-tax states, but the issue remains unsettled. The current SALT cap is $10,000 a year, and a handful of Republicans wanted to boost it to $40,000 a year. The final draft includes a $40,000 cap, but limits it for five years.