WASHINGTON—A small-business loan program designed to back workers’ paychecks has exhausted most of its funding, ramping up pressure on congressional Democrats and Republicans aligned with the White House to reach a deal on the next round of economic aid amid the coronavirus crisis.

Negotiations between Congress and the White House over replenishing the small-business program resumed Wednesday.

The Paycheck Protection Program was on track to exhaust most of its initial allocation of $350 billion in the early morning hours Thursday, with the Small Business Administration saying it had approved more than 1.5 million loans valued at more than $324 billion as of late Wednesday and loans were continuing to be processed.

The fund needs about $10 billion to cover processing and fees, Senate Small Business Committee Chairman Marco Rubio (R., Fla.) said on Twitter.

“The fund being exhausted clearly puts pressure on Congress to act and come to a reasonable conclusion,” said Rep. Patrick McHenry of North Carolina, the top Republican on the House Financial Services Committee. “Every day that passes that we don’t fund this program, more pain is felt by small-business folks and their employees.”