Earlier this month, Sen. James Inhofe, R-Okla., went further, saying in an interview with "The Rusty Humphries Show" that President Obama could be impeached over what he called the "cover-up" after the attack in Benghazi, Libya.
"People may be starting to use the I-word before too long," Inhofe, the top Republican on the Senate Armed Services Committee, said to Humphries. "The I-word meaning impeachment?" Humphries asked, to which Inhofe answered, "Yeah."
"Of all the great cover-ups in history: the Pentagon papers, Iran-Contra, Watergate, all the rest of them, this ... is going to go down as most egregious cover-up in American history," Inhofe said.
And Rep. Steve King, R-Iowa, compared what he called the "cover up" of the attack in Benghazi to Watergate.
"The Obama administration's cover-up of the Sept. 11, 2012, Benghazi terrorist attack surpasses Watergate," King wrote in an op-ed in U.S. News and World Report earlier this month. "When the President of the United States uses the full faith and credit of his office to misinform the American people, we demand the full truth, the whole truth and nothing but the truth."
Despite the scandals, a new ABC News/Washington Post poll out Tuesday found Obama's approval rating holding steady, although at 51 percent.
The survey shows him being helped by accelerating economic optimism as well as by the comparison with the much less-popular Republicans in Congress.
The poll may show Obama is not taking on water, but it's clear Americans do care about these scandals and are critical of them, though.
According to the poll, 74 percent of Americans call the scrutiny of conservative groups by the IRS inappropriate, with 56 percent seeing it as "deliberate harassment," compared to 31 percent who believe it was an "administrative mistake."
With regard to the Benghazi attack, 55 percent of Americans suspect an administration cover-up, and Americans by 54-38 percent say they think the government is doing more to threaten the rights of average Americans than to protect those rights.
There are other Republicans, of course, joining the call to stress prudence. Sen. Rand Paul, R-Ky., spoke to reporters ahead of a GOP fundraiser in New Hampshire with Priebus and said talk of impeachment over the IRS scandal is premature.
"We need to figure out the truth of what happened before we go anywhere else," Paul said, standing with Priebus, who called it "just the beginning."
"It's certainly not the end," Priebus said. "And I'm sure there's going to be a lot more to it. We'll see how far it goes. We'll see how high it goes, too."
George Will said on ABC's This Week Sunday that impeachment talk is "silly."
"That's silly," Will said. "And it is possible to go too far. But Republicans perhaps cannot be blamed for saying a crisis is a terrible thing to waste. And there's a crisis of confidence and they are the political party that exists to say that government is necessary but always is a danger."
Even former House Speaker Newt Gingrich, who played a critical role during the Republican-led impeachment of President in Clinton in 1998, cautioned his GOP colleagues about going too far as they sort through these current scandals, calling on them in an interview with NPR last week to be "calm and factual."