Top Congressional Republicans today turned up the heat on Attorney General Eric Holder, while the nation’s top law enforcement official warned of an “impending constitutional crisis.”

Sen. John Cornyn (Texas), who heads the National Republican Senatorial Committee and is a top contender for a leadership position in the next Congress, called on Holder to resign, even as the attorney general told the Senate Judiciary Committee that he was ready to make major concessions to Republicans investigating “Fast and Furious,” a botched gun-smuggling operation.

At the same time, Speaker John Boehner (R-Ohio) said he would rebuff Holder’s recent offers to meet with House GOP leaders until Holder produces Fast and Furious documents demanded by House Oversight and Government Reform Chairman Darrell Issa (R-Calif.).

The resignation call came at a hearing in which GOP Senators unloaded on Holder over national security leaks, demanding a special prosecutor rather than the two U.S. attorneys whom Holder appointed to lead an investigation. And it was buffered by Republican Senators taking to the floor at the same time as the Judiciary hearing to demand a special counsel be appointed to investigate leaks.

The Republican pile-on over the two issues, which comes as House Energy and Commerce Chairman Fred Upton (R-Mich.) has been sniping at the Obama White House with a health care investigation, shows a new willingness by the GOP to engage in an all-out assault on Democrats on oversight matters.

“I am prepared to make compromises,” Holder told the panel, but “I’ve got to have a willing partner.” But Republicans were in no mood to give quarter.

Citing the Fast and Furious scandal and recent national security leaks, Cornyn   implied Holder had not been truthful with Congress and said, “It’s more with sorrow than with anger that I would say that you leave me no alternative than to join those that call upon you to resign your office.”

Clearly taken aback, Judiciary Chairman Patrick Leahy (D-Vt.) urged Holder to respond. “Well, Mr. Attorney General, you certainly have the — the right to respond to that. The Senator from Texas has accused you of perjury, which is a criminal offense,” he said.

Holder said that a long statement by Cornyn of the attorney general’s faults was “breathtaking in its inaccuracy” and that “I don’t have any intention of resigning.”

“If you want to talk about Fast and Furious, I’m the attorney general that put an end to the misguided tactics that were used in Fast and Furious,” Holder said.

Cornyn’s statement came one day after Issa scheduled a committee vote on holding Holder in contempt of Congress and established a clear universe of documents that the Justice Department could provide to avoid that vote.

At the same time that the attorney general was testifying in the Senate, Boehner laid down his own marker.

“The Speaker will meet with the attorney general when the attorney general complies with the reasonable, specific requests in the May 18 letter from House leaders and Chairman Issa,” a Boehner spokesman said.

On the floor, Republicans rebuked Holder for the leaks investigation, which they argued should be done by a special prosecutor, not by political appointees of President Barack Obama.

Sen. John McCain continued criticism he began last week, railing that national security had been politicized to boost Obama’s re-election efforts.

The Arizona Republican introduced a resolution urging Holder to appoint a special counsel to investigate and for the president to review the results of that effort to determine whether national security was breached and how “damage can be mitigated.”

Democrats blocked the measure.

At the Senate Judiciary Committee hearing, Holder strongly defended Ronald Machen and Rod Rosenstein, the two U.S. attorneys he selected. He said they had the independence and “moxie” to follow the leads wherever the investigation takes them.

Holder argued that he decided against a special prosecutor because it would take too long and there is an urgent need to find who leaked classified information.

Democrats, including Senate Intelligence Chairman Dianne Feinstein (Calif.) and Sen. Sheldon Whitehouse (R.I.), backed Holder’s decision. Feinstein said a fight over how to investigate the leaks would set back the investigation, while Whitehouse, a former U.S. attorney himself, defended the ability of career prosecutors to conduct an independent probe free of influence from the White House or other executive branch officials.

Cornyn doubled down on his calls for Holder to resign after the Republicans’ weekly caucus lunch later in the day, saying the attorney general does not meet “high standards required of that very important office.”

Among GOP leaders, Cornyn led the charge in questioning the impartiality of the two U.S. attorneys. At their closed-door lunch, Senate Republicans discussed Holder and how to continue their challenge to the administration, according to aides familiar with the discussion. Cornyn later went to the floor to continue his criticism of Holder.

However, when Senate Minority Leader Mitch McConnell (R-Ky.) was pressed on the issue, he declined to say whether he agreed with Cornyn’s position that Holder should resign.

“We certainly need to have an investigation of what has happened, and I think John Cornyn speaks for a lot of us as to the frustration we feel about not only the national security leaks, the Fast and Furious matter. There’s been a whole litany of problems coming out of the Justice Department,” McConnell said, noting that he “is listening carefully to what my colleagues are saying.”

Democrats, while leery, are defending Holder against what they believe are purely partisan attacks.

“This whole episode in the last few days by my Republican friends has been a strictly partisan, insincere attempt to embarrass the president,” Senate Majority Leader Harry Reid (Nev.) said.

Sen. Charles Schumer (N.Y.), the Democrats’ messaging chief, took a more tempered approach.

“If we find that some high officials are not giving proper information to your investigators, that kind of lack of cooperation might merit a special counsel, but we aren’t at that point yet,” Schumer said in a statement.

Other Republicans backed Boehner’s position.

“Attorney General Holder sounded willing to negotiate over releasing documents. That’s fine if the offer isn’t hollow. We’ve been talking for a year and a half. A show of good faith would be to produce the documents in question,” Senate Judiciary ranking member Chuck Grassley (R-Iowa) said.

But the two sides seem stuck.

GOP officials have been frustrated by the staff-level talks with the Justice Department because officials “won’t articulate what documents they will release or what portion of documents they’ll release,” a Republican aide said.

The DOJ, noting that Issa has frequently changed the scope of his demands, said the meeting is necessary to nail down exactly what will satisfy the California Republican and what the two parties are agreeing to, whether it is putting contempt off the table permanently or just delaying it.

“I am willing to sit down and talk about the provision of more materials. I have sent letters in that regard, the deputy attorney general has sent letters in that regard, and have not had responses, which leads me to believe that the desire here is not for an accommodation, but for a political point-making,” Holder said.