Senate Republicans scrambled on Tuesday to ensure support for a budget resolution vital to President Donald Trump's drive to overhaul the U.S. tax code, as one Republican fiscal hawk announced he might vote against the measure.

As the Senate opened debate on the fiscal year 2018 budget, Senator Rand Paul objected to spending levels that he said would exceed agreed caps by $43 billion and called for spending reforms for so-called entitlement programs such as the Medicare and Medicaid health insurance programs.

"I will not vote for the budget unless it keeps within the spending caps," the Republican senator told reporters. In a conversation with Trump earlier on Tuesday, Paul said he told the Republican president: "I'm all in. I want to be supportive. I'm a 'yes' vote. But we have to obey our own rules."

Senate Republican aides denied that the budget resolution exceeds federal spending caps set by the Budget Control Act of 2011. Paul said the excess spending was for overseas military operations, which aides said is not subject to caps.

The budget resolution already had a narrow path to passage in the Senate, where Democrats oppose the measures and Republicans have only a 52-48 majority. A "no" vote from Paul appeared to put the budget a single vote from failure, threatening to upend Trump's drive for tax reform.

Another fiscal hawk, Senator Ted Cruz, has refused to disclose whether he would support the measure.

However, the Republican odds of passing a budget resolution improved unexpectedly when Senator Thad Cochran returned to the Senate despite an illness and said in a statement that he looked forward to "taking part in the debate on the budget and tax cuts." A day earlier, Cochran's office had said he would not be available this week.

With Cochran in the Senate, Republicans can pass the measure even if they lose two votes.

The budget resolution is essential to Trump's tax reform strategy because it would unlock a legislative tool known as reconciliation, which would allow Senate Republicans to pass a tax bill with a simple majority. Without it, a partisan tax bill would need 60 votes in the 100-member Senate and would almost certainly fail.

The Republican effort had gained momentum on Monday when two other potential Senate Republican "no" votes — Susan Collins and Lisa Murkowski — indicated they were leaning toward "yes." Senator John McCain also said he would support the budget resolution.

After failing to overturn Obamacare earlier this year, Republicans fear they will face a backlash from constituents in next year's congressional midterm elections if they are unable to pass legislation to cut taxes for businesses and individuals.

Trump and top Republicans have proposed a plan to deliver up to $6 trillion in tax cuts over the next 10 years as part of a reform package that they say will boost economic growth and provide more jobs and higher wages.

Democrats, who criticize the Republican plan as a giveaway to the wealthy, will likely propose numerous amendments to the budget plan to prevent tax cuts for the rich and require legislation that would not expand the federal deficit.

"We're talking about a major political party now working night and day on behalf of the top 0.1 percent," Senator Bernie Sanders, an independent who caucuses with Democrats, told Reuters on Tuesday.

Both the Senate and the House of Representatives must agree on a budget resolution. The House has already approved a different version, so House and Senate Republicans would need to hammer out a unified version and pass it before reconciliation could take effect.