House Majority Whip Kevin McCarthy, the chamber's No. 3 Republican, called for embattled Veterans Affairs Secretary Eric Shinseki to resign, saying the retired four-star general's scandal-plagued agency has become a "national embarrassment."

The California lawmaker is the House's highest-ranking leader to demand Shinseki's ouster.

Shinseki "has served his country with honor and integrity. No one doubts his dedication to our nation’s veterans," said McCarthy in a prepared statement Thursday. "However, the current state of the VA is wholly unacceptable and has become a national embarrassment — it requires immediate action."

McCarthy said new leadership at the VA is imperative to "fixing the wrong that this massive bureaucracy has done to the men and women we owe so much to."

"Therefore, today, I call on General Shinseki to do what is right and step aside as secretary effective immediately," he said.

The agency's inspector general's office this week reported that 26 VA facilities are being investigated nationwide, including a Phoenix hospital where 40 veterans reportedly died while waiting for treatment as staff there kept a secret list of patients waiting for appointments to hide delays in care.

Earlier Thursday, House Speaker John Boehner, R-Ohio, said he is "getting a little closer" to calling for Shinseki to step down -- though he added that firing Shinseki won't solve the VA's systemic problems.

"This isn't about one person. This isn't about the secretary. It's about the entire system underneath him," Boehner said.

House Minority Leader Nancy Pelosi, D-Calif., also has stopped short of demanding Shinseki's head, though she suggested Congress should investigate the scandal-plagued VA.

But rumblings for Shinseki's outster are growing among rank-and-file lawmakers.

"The first person we need to fire is the secretary of Veterans Affairs, Mr. Shinseki himself," Rep. David Scott, D-Ga., said on the House floor Wednesday. "We respect him. We respect his sacrifice for this country and everything else. But the buck stops at the top."

Fellow Georgia Democrat Rep. John Barrow on Wednesday echoed the call to fire the VA head.

"While I don't think a change in leadership will immediately solve the serious problems that plague the VA, I do think it’s time to give someone else an opportunity to lead the agency and begin the rebuilding process to ensure these issues never happen again," Barrow said.

Across the Capitol, Senate Minority Whip John Cornyn, R-Texas, earlier this month said Shinseki's time as secretary "has come to an end."

"The president needs to find a new leader to lead this organization out of the wilderness, and back to providing the service our veterans deserve," Cornyn said.