By Manu Raju and Ashley Killough CNN

(CNN) -- Republican lawmakers mostly shrugged off Thursday the anonymous senior administration official who sharply criticized the President in an opinion piece for The New York Times.

While some called for the unnamed official to resign, others felt the author's op-ed was less-than-surprising and just the latest example of the chaos in the Trump administration.

Republican Sen. Jerry Moran of Kansas had some concerns.

Story Continues Below

"I like certainty, I like predictability. It seems like something is churning constantly with this administration and in the media," Moran said. "It's important for us to have that stability that comes from a day-to-day White House that operates well."

"I'd love to see the certainty," he continued.

The author of the Times op-ed blasted Trump as an amoral, anti-democratic and incompetent leader, and confessed to being part of an army of senior administration officials "working diligently from within to frustrate parts of (Trump's) agenda and his worst inclinations."

Outgoing Republican Sen. Bob Corker, a Trump critic, said he "didn't think there was any new information that was laid out," adding that he felt it was "a little bit dramatic" and he doesn't like anonymous letters.

Story Continues Below

"I mean anyone who's had any dealings over there knows that this is the reality that we're living in and so I don't know -- I think a lot's been made out of nothing," Corker said. "I think the biggest issue they're going to have is figuring out who wouldn't have written a letter like that."

Another retiring critic of Trump, Sen. Jeff Flake, also felt it was par for the course that a senior administration official disapproved of the President's actions and rhetoric.

"I hope more will come out publicly and I hope that the Congress will more publicly condemn statements like the President made and on Twitter on Monday," he said.

Sen. John Cornyn, a Texas Republican and the second ranking GOP member of the chamber, shook his head "no" when reporters asked if he was concerned about the President's stability.

Story Continues Below

"A number of us have given the President some friendly advice, like on the Twitter account and the like," he said, when pressed whether Trump should take more stock in some of the criticism from the op-ed. "But he's convinced that actually helped him getting elected president and he enjoys communicating directly with the American people and in the end he's going to be the one that makes that decision. Yes, we try to give him advice in that area and he rejected it."

Over in the House, Republicans were more frank. House Speaker Paul Ryan said the person who wrote the op-ed is "living in dishonesty" and "shouldn't work for the President."

"A person who works in the administration serves at the pleasure of the President. It's a person who obviously is living in dishonesty," he told reporters. "That doesn't help the President, so if you're not interested in helping the President, you shouldn't work for the President."

Story Continues Below

Asked if Congress has any role in investigating who was behind the op-ed, Ryan said, "Not that I know of."

Rep. Mark Meadows, a Trump ally and chairman of the House Freedom Caucus, disagrees.

As chairman of the Oversight Subcommittee on Government Operations, Meadows told reporters that he and his staff are looking into whether this was something they could investigate.

"We're less than 24 hours into this," he said. "Do I take it seriously? Certainly. Should we all take it seriously? Without a doubt."

He admitted, however, there were no concrete steps at this point for an official probe.

Meanwhile, Sen. Rand Paul suggested using a lie detector test to determine the author's identity.

"I think if you have a security clearance in the White House I think it would be acceptable to use a lie detector test and ask people whether they are talking to the media against the policy of the White House," the Kentucky Republican said. "This could be very dangerous if the person who is talking to the media is actually revealing national security secrets, so yes I think we need to get to the bottom of it."

CNN's Kristin Wilson, Liz Landers, and Ted Barrett contributed to this report.

TM & © 2018 Cable News Network, Inc., a Time Warner Company. All rights reserved.