Attorney General Eric Holder. (J. Scott Applewhite, Associated Press)

Sen. John McCain (R-Ariz.) said Sunday that Attorney General Eric Holder needs to ask himself whether he can continue to serve in his current position, while other Republicans continued leveling criticism against the Justice Department's top official.

"The Attorney General has to ask himself the question, 'Is he really able to effectively serve the president of the United States and the American people under the present circumstances?' That’s a decision he’d have to make," McCain said on CBS's "Face The Nation."

When pressed about whether he thinks Holder should resign, McCain said that is up to

Holder. "I think it would be tough for him to answer the question whether he can still effectively serve the president of the United States," McCain said.

As Republicans pounced, Democrats defended the attorney general. The Senate's third-ranking Democrat said he believes Holder will stay on as attorney general. "I haven't seen anything that would prevent him from continuing to do his job," Sen. Charles E. Schumer (D-N.Y.) said on NBC's "Meet The Press." Schumer said both he and President Obama have confidence in Holder.

"I don't think he should step aside," echoed Sen. Jack Reed (D-R.I.).

Holder has come under fresh scrutiny over recent congressional testimony on the subject of investigating journalists. At issue is whether Holder's recent remarks before a House Committee are at odds with what he knew about an investigation involving a Fox News journalist. McCain said Holder should be given the chance to explain "obvious contradictions."

Other Republicans on Sunday kept up a drumbeat of GOP criticism directed at Holder.

"I think the attorney general has definitely lost the trust of the American people," said Rep. Marsha Blackburn (R-Tenn.) on "Meet The Press."

Republican National Committee Chairman Reince Priebus said on "Fox News Sunday" that Holder "is not representing the American people. He is representing the Democratic Party."

Like McCain, House Intelligence Committee Chairman Mike Rogers (R-Mich.) and House Government Oversight Committee Chairman Darrell Issa (R-Calif.) stopped short of calling on Holder to resign.

At a recent appearance before the House Judiciary Committee, Holder said the potential prosecution of a journalist reporting sensitive information is "not something that I have ever been involved in, or would think would be a wise policy."

But a subsequent Washington Post report about a Justice Department investigation into possible leaks of classified information about North Korea to Fox News reporter James Rosen has spurred Republicans to question whether Holder was telling the truth. Law enforcement officials characterized Rosen as a possible “co-conspirator” and multiple reports say that Holder was personally involved in signing off on the Rosen warrant.

House Judiciary Committee Chairman Bob Goodlatte (R-Va.) and Rep. James Sensenbrenner (R-Wis.) sent Holder a letter last week asking for clarification about his remarks. The Republicans have given Holder until Wednesday to respond.

Goodlatte said Sunday that the conflict between Holder's remarks and his involvement in the Rosen matter is "very troublesome" but that the attorney general's response must be reviewed before the question of whether Holder lied is ultimately answered.

"We also think it's very important the attorney general be afforded the opportunity to respond," Goodlatte said.

Rep. Chris Van Hollen (D-Md.) said Holder's recent testimony that he had never been involved in the potential prosecution of a journalist for disclosing sensitive material is consistent with his role in the investigation of Rosen.

"These are perfectly consistent. It is oft in the practice in cases where you have investigations that you target somebody for the purpose of gathering information with never having any intention of prosecuting them," Van Hollen said on "Fox News Sunday."

"I don't think there's perjury. There's been no prosecution or attempt at prosecution of any journalist so there can't be perjury," Schumer said.

Goodlatte said the cases involving Rosen and the decision to secretly obtain phone records from Associated Press journalists has undermined the Justice Department's ability to investigate leaks.

"I would argue that both in the mishandling of this case and the AP case, the Justice Department has damaged their ability to investigate leaks properly because they haven't followed the rules, and in this case the attorney general has to answer for it in particular," Goodlatte said.

Updated at 11:58 a.m.