WASHINGTON—The Senate approved a short-term extension of transportation programs Saturday, sending to President Biden stopgap legislation after the House again delayed a vote on a roughly $1 trillion infrastructure bill.

The 30-day extension of the transportation programs effectively creates a new deadline for Democrats to resolve divisions that have held up the $1 trillion infrastructure bill in the House. Mr. Biden on Friday called on House Democrats to hold off on approving the public-works legislation, which passed the...

WASHINGTON—The Senate approved a short-term extension of transportation programs Saturday, sending to President Biden stopgap legislation after the House again delayed a vote on a roughly $1 trillion infrastructure bill.

The 30-day extension of the transportation programs effectively creates a new deadline for Democrats to resolve divisions that have held up the $1 trillion infrastructure bill in the House. Mr. Biden on Friday called on House Democrats to hold off on approving the public-works legislation, which passed the Senate this summer with broad bipartisan support, until the party first unifies around a broader social policy and climate proposal.

Failure by the House to pass the infrastructure bill by Oct. 1 led to a lapse in authorization for federal transportation programs, temporarily putting roughly 3,700 Transportation Department employees on furlough. The short-term patch, which the House passed on Friday instead of the infrastructure bill, temporarily reauthorizes those programs. The Senate approved the measure by unanimous consent Saturday afternoon.

For Democrats, the linking of the infrastructure bill and the social policy and climate effort is the result of a demand by progressives in the party, who see threatening to block the infrastructure bill as a way to pressure centrists to ultimately support the social policy and climate package. Centrists, including Sens. Joe Manchin (D., W.Va.) and Kyrsten Sinema (D., Ariz.), have raised concerns about the size of the healthcare, education, and climate bill and the tax increases proposed to pay for it.

Mr. Biden and other top Democrats scrambled this week to negotiate an agreement with centrists on the social policy and climate bill and, in turn, mollify progressive concerns about passing the infrastructure bill. Those efforts didn’t wrap up by Friday, and House Speaker Nancy Pelosi (D., Calif.) again delayed a vote on the infrastructure bill.

“Clearly, the Bipartisan Infrastructure bill will pass once we have agreement” on the social policy and climate bill, Mrs. Pelosi wrote to House Democrats on Friday.

The delay in passing the infrastructure bill in the House has frustrated centrist Democrats, whose support will be critical for Democrats to pass the social policy and climate bill with their very narrow majorities in Congress. Democrats had proposed spending $3.5 trillion for the broader bill, though Mr. Biden told House Democrats on Friday that the top line would likely land around $2 trillion after negotiations with centrists.

Ms. Sinema, who holds major sway over the negotiations in the 50-50 Senate, called the delayed vote “deeply disappointing” in a statement Saturday. She said the decision had frayed trust among Democrats in the ongoing policy negotiations.

“Canceling the infrastructure vote further erodes that trust,” she said.

White House press secretary Jen Psaki said in a statement Saturday that Mr. Biden left Friday’s discussions “with the firm belief that there was a shared commitment from across the Democratic Caucus to deliver for the American people.”

Write to Andrew Duehren at andrew.duehren@wsj.com