Cruz's comments during a radio interview on Monday follow Obama dining with a dozen of Cruz's Republican Senate colleagues on Wednesday. The president is scheduled to meet with both Republican and Democratic caucuses in the House and the Senate during the week.

"I think we should always be willing to listen. I think we should always treat each other with civility and respect," Cruz, a Tea Party favorite, said Monday during an interview on The Bill Bennett Show. "I'm glad that he is reaching out. That is better than what I have seen the first couple of months here where it seemed that he had no interest whatsoever in talking with the other side."

During the dinner on Wednesday Obama told the group of Republican senators that he wanted to finish a grand bargain plan for reducing the deficit by the end of July. Participants leaving the meeting seemed optimistic about the possibility of completing a grand bargain.

Cruz added though that he would like to see more from Obama than just sitting down and listening to Republicans.

"But I'm a big believer that actions speak louder than words —that if he's really interested," Cruz said.  "The day I was elected to office I said I look forward and am eager to work with President Obama if he's willing to get serious about solving the grave economic and fiscal challenges."