By Susan Cornwell and David Morgan

WASHINGTON, Oct 1 (Reuters) - The Democratic-controlled U.S. Congress on Friday was struggling to reach an agreement on President Joe Biden's sweeping agenda, with House of Representatives Speaker Nancy Pelosi vowing to hold a vote on a $1 trillion infrastructure bill.

That promise came shortly after midnight -- after a day of negotiations with the party's moderate and progressive wings failed to reach a deal on a larger companion bill including social spending and addressing climate change.

"We'll vote today," Pelosi told reporters as she left the U.S. Capitol. A similar promise by the speaker on Thursday was not fulfilled.

The Senate in a bipartisan August vote passed the $1 trillion bill, which includes funds for roads, bridges and other infrastructure. Moderates had pushed for a vote this week while progressives insisted they would not approve the bill without agreement on a companion bill that Senate Democrats intend to pass without Republican votes.

With razor-thin majorities in Congress, Biden's Democrats need almost total unity to pass legislation. Republicans are unlikely to help, eager to deny Biden a policy victory ahead of the 2022 midterm elections, when history favors their chances to recapture majorities.

Faced with increasingly stiff odds of passing their $3.5 trillion social spending proposal, Biden and his aides are trying to find out what narrower proposal could unite an ideologically fractured Democratic caucus of lawmakers, according to people familiar with the matter.

Lawmakers on the party's left flank have said they will not vote for the infrastructure bill unless they feel certain their priorities will be reflected in the social spending bill.

Democratic Representative Ilhan Omar, a leading House progressive, told reporters on Thursday: "Nothing has changed with our caucus members. We don't have the votes to pass infrastructure."

Moderate Democratic Senator Joe Manchin has proposed a spending package of about $1.5 trillion. Another Democratic moderate, Senator Kyrsten Sinema, declined to say whether she agreed with Manchin's proposal. She has met with Biden multiple times to discuss the bill.

DEBT-CEILING THREAT

In yet another high-stakes battle, congressional Democrats and Republicans continue brawling over giving the Treasury Department additional borrowing authority beyond the current statutory limit of $28.4 trillion. A historic U.S. debt default could occur around Oct. 18, Treasury Secretary Janet Yellen has estimated, if Congress fails to act.

Republicans want no part of the debt limit increase, saying it is Democrats' problem since they control Congress and the White House. Democrats note that about $5 trillion of the nation's debt is the result of tax cuts and spending passed during Republican Donald Trump's presidency.

The House approved a bill late on Wednesday suspending the debt limit through December 2022. The Senate could vote on it "as early as next week," Senate Majority Leader Chuck Schumer said, but Republicans are expected to block it again.

(Reporting by David Morgan, Susan Cornwell and Richard Cowan Editing by Scott Malone and Peter Graff)