By Susan Cornwell and David Morgan

WASHINGTON (Reuters) - The Obama administration and U.S. Senate Republican leaders scrambled on Tuesday to garner enough support to get a Puerto Rico debt relief bill through a critical procedural vote set for Wednesday which several lawmakers predicted would be close.

After months of waiting for Congress to act as Puerto Rico's economic crisis progressively worsened, the Caribbean island appeared to be on the verge of securing a relief plan from Washington aimed at helping it address a hobbling $70 billion debt.

The leaders of both political parties in the Senate are on board, but the outcome appeared uncertain.

The Obama administration sent Treasury Secretary Jack Lew to Capitol Hill on Tuesday to try to persuade recalcitrant Democrats, while Republicans heard arguments for the legislation from fellow senators at a closed-door luncheon.

"We will win the vote tomorrow," said Senator Bill Nelson, a Florida Democrat, as he left the meeting with Lew.

Senate Majority Leader Mitch McConnell, a Republican, told reporters he was "very much on board," and was urging Republicans to back the measure establishing a federal oversight board to be in charge of restructuring the U.S. territory's debt.

"I'm hopeful and optimistic that the (Obama) administration will be able to get Democrats on board, and we believe strongly that it’s an approach that appeals to most Republicans," McConnell said.

Senate Democratic Leader Harry Reid said he would support the bill. The Senate Democratic whip, Dick Durbin of Illinois, a recent convert to the proposal, said he was trying to get a majority of Democrats to back it.

House Democratic leader Nancy Pelosi added that while there is much to the legislation she objected to, she implored her Senate colleagues to adopt the bill. "Failure to pass this bill would be a tremendous win for the unscrupulous hedge funds that have held this bill up for six months demanding to be first in line over the needs of the people of Puerto Rico," she said.

"Unless Congress acts, our fellow Americans in Puerto Rico will be plunged into deep economic turmoil in just three days’ time."

Puerto Rico's 3.5 million residents are U.S. citizens. The U.S. territory is reeling from a 45 percent poverty rate, a steady flow of outward migration to the U.S. mainland that further shrinks its tax base and the shuttering of essential services.

But Durbin predicted "it will be close" Wednesday morning, when the Puerto Rico debt relief bill will need a supermajority of 60 senators' votes to stay alive in the Senate.

And despite McConnell's expression of optimism, other Republicans said the leadership appeared worried behind the scenes.

"I think leadership is concerned because they're really whipping it," said Senator Dean Heller, a Nevada Republican. "When they whipped me last night, I said 'no'. So they're coming back and asking if I'll reconsider."

JOINING THE FRAY

The White House joined the fray, with spokesman Josh Earnest saying that without action by Congress to help Puerto Rico deal with its debt, the need for a bailout of the U.S. territory will become more likely.

The measure is identical to the plan passed by the House of Representatives earlier this month, as Congress tries to send it to President Barack Obama to sign into law by July 1. That is when Puerto Rico faces a potential default on a chunk of its debt if it cannot make $1.9 billion in payments.

If the Wednesday morning procedural vote is successful, it would clear the measure for passage this week.

But Republican skeptics of the bill are worried it could constitute a bailout - something its supporters deny - while Democrats have expressed concern about the composition of the oversight board and labor provisions that they say could lower minimum wages for young workers in Puerto Rico.

The top Democrat on the Senate Finance committee, Oregon's Ron Wyden, announced Tuesday he would back the legislation. But Ohio Democratic Senator Sherrod Brown appeared to be wavering even after meeting with Lew, Wyden and other Democrats in a Senate office building.

Brown said he would be more likely to vote "yes" in Wednesday's procedural vote if Senate leaders promise him a vote on an unrelated issue - legislation to ensure that the federal government and coal mine operators honor payment of promised pensions and health benefits to retired miners.

Lew said he thought there was "broad understanding" of the urgency. "I just do not believe that we can let three and a half million Americans descend into chaos," he said.

(Additional reporting by David Lawder and Isma'il Kushkush; Editing by Daniel Bases and Matthew Lewis)