By David Morgan, Richard Cowan and Patricia Zengerle

WASHINGTON (Reuters) -The Democratic-led U.S. Senate on Monday set the stage for final passage of a $95.34 billion aid package for Ukraine, Israel and Taiwan, amid growing doubts about the fate of the legislation in the Republican-controlled House of Representatives.

The Senate voted 66-33, exceeding a 60-vote margin, to sweep aside the last procedural hurdle and limit debate on the measure to a final 30 hours before a vote on passage that could come on Wednesday.

But things could move more quickly. Republican opponents of the legislation were due to speak against it on the Senate overnight, aides said. Such a move that could enable Senate Majority Leader Chuck Schumer to move for final passage Tuesday morning.

Passage would only send the legislation on to the House, where Speaker Mike Johnson said his Republican majority wanted the legislation to include conservative provisions to address the flow of migrants across the U.S.-Mexico border.

“In the absence of having received any single border policy change from the Senate, the House will have to continue to work its own will on these important matters,” Johnson said in a statement issued just before the Senate started voting.

“America deserves better than the Senate’s status quo,” said Johnson, who has suggested in the past that the House could split the legislation into separate bills.

Republicans had demanded for months that the aid package would need to include insisted that any additional aid to Israel and Ukraine must also address the high numbers of migrants arriving at the U.S-Mexico border.

Democratic President Joe Biden has been urging Congress to hurry new aid to Ukraine and U.S. partners in the Indo-Pacific, including Taiwan, for months. After Hamas’ Oct. 7 attack on Israel he also requested funds for the U.S. ally, along with humanitarian aid for Palestinians in Gaza.

Ukrainian officials have warned of weapons shortages at a time when Russia is pressing ahead with renewed attacks.

But to become law the bill must pass the House as well as the Senate, and the House has not passed any major aid for Ukraine since Republicans took control of the chamber in January 2023.

MAYORKAS IMPEACHMENT

For months, Republicans had insisted that any additional aid to Israel and Ukraine must also address the high numbers of migrants arriving at the U.S-Mexico border.

But last week, at the urging of former President Donald Trump, most Senate Republicans voted to kill a bipartisan security bill that had been crafted over four months and was seen as the most significant border security and immigration reform effort in at least a decade.

The House instead this week is expected to try again to impeach Biden’s Homeland Security Secretary, Alejandro Mayorkas, the top official responsible for the border.

Schumer stripped the border security language from the bill last week.

Some Republican senators, including those most closely allied with Trump, have called for another overhaul of the bill.

Senator Lindsey Graham said portions of the U.S. aid should be converted into loans and only “lethal aid,” not humanitarian aid, be included in the package. And he called for U.S. border security provisions, although so far his party has not unveiled border-related amendments.

(Reporting by David Morgan, Richard Cowan and Patricia Zengerle; Additional reporting by Makini Brice and Katharine JacksonEditing by Don Durfee and Rosalba O’Brien)