"Do we have the votes for health care? I think we do," Cohn said in an interview with "CBS This Morning" during a special broadcast live from the White House. Cohn serves as the director of the National Economic Council.

"We're going to get health care down to the floor of the House," he added. "We're convinced we've got the votes and we're going to keep moving on with our agenda."

During a separate interview on "CBS This Morning," Priebus was also asked if a health care bill will happen this week.

"I certainly hope so," he said. "I think it will happen this week," adding that it would be "one of the fastest pieces of signature legislation to go through for a president since Roosevelt."