Appearing on CBS' "Face the Nation," Senate Minority Whip John Cornyn of Texas noted the White House has said the president did not know about scandals involving the Internal Revenue Service and Justice Department seizure of journalists' telephone records until the matter became public.
Cornyn said he found that "implausible."
"It seems to be the answer of the administration, whenever they're caught doing something they shouldn't be doing, is, 'I didn't know about it,' and it caused me to wonder whether they believe willful ignorance is a defense when it's your job to know," Cornyn said.
"So I really think it is a culture of coverups and intimidation that is getting the administration in so much trouble," Cornyn said.
His comments came after a week during which the White House has been barraged with questions about its handling of the attack on a U.S. mission in Benghazi, Libya, the Justice Department's seizure of phone records from the Associated Press and the investigation of the IRS.
He predicted high-level officials will be forced to resign as a result of IRS employees at a field office in Cincinnati singling out conservative groups for extra scrutiny when evaluating applications for tax-exempt status.
So far, two Ohio-based IRS employees have been disciplined in wake of the scandal, and Acting Commissioner Steven Miller stepped down last week.
"So, I have a very hard time believing that this was something cooked up in Cincinnati from mid-level employees at the IRS. That's just implausible," he said.