Liberal groups rallied around Harvard law professor Elizabeth Warren on Wednesday and renewed calls for her to lead the fledgling consumer watchdog agency, a day after she was accused of lying in a contentious congressional hearing.

An online petition circulated by the Campaign for America’s Future asking the White House to appoint her while the Senate is in recess garnered 20,000 signatures by Wednesday afternoon. A similar effort from Progressive Change Campaign Committee signed up 10,000 people an hour in the first five hours, organizers said, and won support from Sen. Al Franken (D-Minn.).

“We have momentum, President Obama is paying attention, and an outpouring of national support will make a big difference,” Franken wrote in a letter to constituents released Wednesday.

The Consumer Financial Protection Bureau was created as part of sweeping reforms of the nation’s banking system that Congress passed last year. The White House tapped Warren to help set up the agency but has not named her — or anyone else — to lead it. The agency is slated to open for business July 21, but it will have limited authority if no director is in place.

Warren has been Democrats’ top pick for the job, and she is credited with coming up with the idea for the agency several years ago. But this month, 44 Republican senators vowed to block any nominee unless significant changes were made to the agency’s structure. Three bills pending in the House would create a five-member board of directors to run the CFPB, impose tougher oversight of the agency by existing banking regulators and subject it to the appropriations process. Currently, the CFPB’s budget is carved from the Federal Reserve’s.

The debate turned personal in a House subcommittee hearing Tuesday that ended with a spat between Warren and Rep. Patrick T. McHenry (R-N.C.) over how long the meeting should last.

Warren accused McHenry of disregarding her schedule by extending the hearing beyond an hour.

“Congressman, you are causing problems,” she said.

McHenry said she was “making up” any agreement between their staffs to limit the time of her testimony, and on Wednesday, he released e-mails to make his case.

“I was shocked by Ms. Warren’s blatant sense of entitlement,” he said in a statement after the hearing. “This is just further example of her disregard for congressional oversight.”

Treasury Secretary Timothy F. Geithner came to Warren’s defense Wednesday at a breakfast held by Politico. He criticized Republicans’ effort to weaken financial reforms by holding up appointments and called their opposition to key confirmations — including Warren’s —“untenable.”

“I thought what happened yesterday was deeply unfair to her personally,” he said. “How much is political theater? How much is the necessary tough job that Congress must do?”

Liberal activists took their campaign online Wednesday, creating a new group on Facebook called Citizens Against Patrick McHenry that drew more than 700 supporters. They also took over McHenry’s official Facebook page by posting hundreds of vitriolic comments.

Rep. Jackie Speier (D-Calif.) called on McHenry to apologize.

The exchange between Warren and McHenry was “a scene that had it happened in a junior high student council meeting would have been stopped by the faculty adviser,” she said.