Republicans were swarmed on Tuesday with questions about what President Donald Trump knew and when did he know about former national security adviser Michael Flynn’s questionable interactions with Russian authorities. But there was little consensus on the best venue for getting to the bottom of it.

“I think it’s good for the American people to understand, in a fulsome way, everything that’s happened. And to get it behind us,” Senate Foreign Relations Chairman Bob Corker said. “This is going to go on forever if we don’t address it somehow.”

But just a few hours removed from Flynn’s resignation following reports that he misled Vice President Mike Pence and other senior White House officials about his conversations with Russia’s U.S. ambassador, Sergey Kislyak, there was no party line in the GOP about exactly how to proceed.

Senate Majority Leader Mitch McConnell came to the floor Tuesday morning and did not mention Flynn, choosing to instead discuss Cabinet nomination politics. McConnell has previously stated that allegations of Russian misconduct in last fall’s election would be the purview of the Senate Intelligence Committee.

His deputy, Senate Majority Whip John Cornyn of Texas, said in the Capitol on Tuesday he expects the House and Senate Intelligence committees will conduct an investigation into Flynn’s contacts with the Russians, an addition to what they have already been looking at concerning the Kremlin. Cornyn is a member of the Intelligence panel.

The Texas Republican did, however, say he didn’t think the Flynn issue was symbolic of broader dysfunction within the administration.

“I think it’s symbolic of somebody with a distinguished military career making a bad mistake,” Cornyn told reporters. 

Corker also said he thought the “Flynn component” would be added on to the existing investigation. 

“I’ve got to believe that certainly the Intelligence committee and others will add this as a component to what they are doing,” the Tennessee Republican said.

Republican Sen. Marco Rubio of Florida, a member of the Intelligence committee, told Roll Call that people should have confidence the committee will conduct a through inquiry of Russian meddling “because if we don’t, I’ll be very angry and I’ll let everyone know about it.”

And that’s what the panel’s ranking Democrat, Sen. Mark Warner of Virginia, certainly wants.

“We have jurisdiction. We are actively working this. We have already started to review the raw intelligence,” Warner said, adding that he would like to see Flynn testify in a public hearing under oath. Corker supported having Flynn testify.

Regarding the administration, Warner said, “I would think they’d want this cloud to be removed and the way to remove this cloud is to get all the information out. … The public deserves to know what happened, how it happened, and what effects it had on the democratic process.”

The chairman of the Intelligence Committee, however, put out a bare-bones statement about the matter, not mentioning any possible future inquiry.

“Mike Flynn served his country with distinction,” North Carolina Sen. Richard M. Burr said. “The president needs a national security adviser whom he can trust and I defer to him to decide who best fills that role.”

Arizona Republican Sen. John McCain, chairman of Senate Armed Services, told reporters the public needs to know whether Trump knew about or ordered Flynn to discuss sanctions with the Russian ambassador. Asked if that question needs to be addressed, he said: “Sure. Any questions that are raised need to be answered.”

Over on the other side of the Capitol, though, House Republican leadership was less pointed in the path forward on investigating Flynn.

Speaker Paul D. Ryan of Wisconsin advocated a go-slow approach.

When pressed on whether Congress or an independent body would seek an investigation into the circumstances of Flynn’s resignation, Ryan said, “I’m not going to prejudge any of the circumstances surrounding this until we have all of the information.”

“The administration will explain the circumstances that led to this,” the speaker said, adding that he would defer to whatever may come out of the Intelligence committees. “The Intelligence committees have been looking into this thing all along, by the way, just involvement with respect to Russia.”

The chairman of the House Intelligence Committee, California Republican Rep. Devin Nunes, put out a statement early Tuesday that did not address any future inquiries.

“Michael Flynn served in the U.S. military for more than three decades. Washington, D.C., can be a rough town for honorable people, and Flynn — who has always been a soldier, not a politician — deserves America’s gratitude and respect for dedicating so much of his life to strengthening our national security. I thank him for his many years of distinguished service,” Nunes said.

Oklahoma Rep. Tom Cole, a veteran hand known for calmly outlining GOP talking points, said he was “always happy to look at what the Russians were doing,” but didn’t offer hints about what was next. 

“Happy to have any investigations that would be appropriate, but I don’t think they’re going to change the outcome of the election,” Cole said. 

Bridget Bowman, Niels Lesniewski, John M. Donnelly, Rema Rahman and Lindsey McPherson contributed to this report.