The leader of Elizabeth Warren's consumer watchdog is in the hot seat.

One of President-elect Donald Trump's first acts in the White House should be firing Consumer Financial Protection Bureau Director Richard Cordray, a pair of Republican Senators argued in a letter on Monday night.

The lawmakers believe the CFPB, which has taken on big banks like Wells Fargo as well as shady payday lenders, has become too powerful since its 2011 inception.

"It's time to fire King Richard," Senator Ben Sasse of Nebraska wrote in a statement.

Sasse and Senator Mike Lee of Utah argued that Cordray's tenure has been "disastrous" because the CFPB has "pursued costly regulatory policies" that have hurt community banks and credit unions.

The Republicans also believe the CFPB's single-director structure is "unconstitutional" -- a belief backed up by a federal court ruling in October.

However, it's not exactly clear if Trump will have the authority under current law to fire Cordray, whose term doesn't expire until July 2018. Dodd-Frank's strict language allows the president to remove the CFPB director only for cause.

"Cordray will probably sue to stay on. Let him sue. It will be an exciting battle," said John Berlau, a senior fellow at the libertarian Competitive Enterprise Institute, who also wants Trump to remove Cordray.

Related: Elizabeth Warren watchdog under siege

The CFPB declined to comment on the GOP letter. The CFPB recently said that Cordray "has no plans to step down" and noted he was confirmed in 2013 by a bipartisan group of 66 senators. That confirmation followed President Obama's controversial recess appointment of Cordray in 2012.

Steven Mnuchin, Trump's pick as treasury secretary, declined through a spokeswoman to comment on "any potential Treasury policies or actions" until after his confirmation hearing.

The back-and-forth over Cordray is the latest evidence that the CFPB, the consumer watchdog conceived by Warren, is under siege following the election.

Trump has promised to roll back regulation broadly, while Republicans have taken specific aim at the CFPB. GOP proposals have called for everything from wiping out the CFPB entirely to yanking its funding or replacing its director with a bipartisan board.

Defenders of the CFPB argue that efforts to defang the regulator are unwise.

Patricia McCoy, a Boston College Law School professor who oversaw CFPB mortgage policy in 2011, said the bureau has been "remarkably successful" under Cordray. She pointed to the CFPB's record-setting $100 million fine against Wells Fargo last September in the fake account fiasco.

Warren didn't respond to a request for comment on the GOP letter. The Massachusetts Senator previously told CNNMoney Republicans and big banks want to "strangle" the CFPB because it's proven to be a strong consumer watchdog.

Senator Sherrod Brown, the leading Democrat on the Senate Banking Committee, said in a statement that "firing Cordray and abolishing" the CFPB would "shatter" Trump's promise to hold Wall Street accountable. Brown praised the CFPB's ability to protect Americans who have been "ripped off" by financial institutions.

Related: Wall Street hates the Volcker Rule. Will Trump kill it?

But some Republicans feel the CFPB doesn't have enough oversight.

Lee and Sasse called the CFPB the "single-most egregious example" of a "headless fourth branch" of independent agencies unaccountable to the public or the president. They pointed to how the CFPB's decision-making authority rests on one person who is removable by the president only for cause.

The Senators cited the October federal court decision that ruled the CFPB is "unconstitutionally structured."

The CFPB has appealed the ruling in an effort to get it reversed.