Senators were voting in a marathon session on Monday night known as a "vote-a-rama," featuring a series of amendments by Republicans and the minority Democrats, part of the arcane process Republicans are using to bypass Senate rules that normally require 60 of the chamber's 100 members to agree on legislation.
But after roughly 12 hours, it was still unclear how long the voting would last. Lawmakers said the process was being held up partly by the need to determine whether amendments complied with special budgetary rules.
Republicans can afford to lose no more than three votes in either chamber to pass a bill the Democrats are united in opposition to.
The nonpartisan Congressional Budget Office released its assessment on Sunday of the bill's hit to the $US36.2 trillion ($A55.1 trillion) US debt pile.
The Senate version is estimated to cost $US3.3 trillion ($A5.trillion), $US800 billion ($A1.2 trillion) more than the version passed last month in the House of Representatives.
Many Republicans dispute that claim, Democrats, meanwhile, hope the latest, eye-widening figure could stoke enough anxiety among fiscally minded conservatives to get them to buck their party, which controls both chambers of Congress.
"This bill, as we have said for months, steals people's healthcare, jacks up their electricity bill to pay for tax breaks for billionaires," Democratic Senate Minority Leader Chuck Schumer said in a speech to the Senate.
Thune countered that the tax cuts will help families and small businesses, as he defended spending reductions to social safety net programs.
He said Medicaid was growing at an unsustainable rate and there were some improvements and reforms to make it more efficient.
The Senate narrowly advanced the tax-cut, immigration, border and military spending bill in a procedural vote late on Saturday, voting 51-49 to open debate on the 940-page megabill.
Trump wants the bill passed before the July 4 Independence Day holiday.
Many of the amendments are from Democrats proposing limiting cuts to Medicaid and abortion services but those and other Democratic amendments so far were rejected by the Republican majority.
Elon Musk, formerly appointed by Trump to spearhead his government cost-cutting plan before the pair had a public falling-out in June over the budget bill, made a flurry of angry posts on X on Monday, threatening to target Republicans ahead of the 2026 mid-term election.
"Every member of Congress who campaigned on reducing government spending and then immediately voted for the biggest debt increase in history should hang their head in shame!," Musk posted on X.
He also reiterated his interest in a new political party and accused lawmakers in both parties of belonging to the "porky pig party," a dig at government spending levels.
The Republican measure contains a $US5 trillion ($A7.6) trillion debt ceiling increase - $US1 trillion ($A1.5 trillion) more than the House's bill - but failure to pass some version would present lawmakers with a serious deadline later this summer, when the Treasury Department could come close to exhausting its borrowing authority and thus risk a devastating default.
The debt limit increase has caused Senator Rand Paul of Kentucky to come out in opposition to the bill, joining fellow Republican Tillis, who decried its cuts to Medicaid and clean energy initiatives.
According to the Congressional Budget Office, the Senate bill would result in about 11.8 million additional uninsured people, surpassing estimates for the House's version.
If the Senate succeeds in passing the bill, it will then go to the House, where members are also divided, with some angry about its cost and others worried about cuts to the Medicaid program.
