In an appearance on NBC's "Meet the Press," Paul was asked whether there are any areas on which he could work this year with President Barack Obama.
"Well, you know, I think the thing we make the mistake of up there is we try to agree to too much," he said. "I'm the first to acknowledge the president and I don't agree on every issue, but if you took 10 issues, I think there are two or three that we agree on, and we agree firmly on, and why don't we go after the issues that we agree on?"
Asked about comments last week by former Arkansas Gov. Mike Huckabee -- who said Democrats "want to insult the women of America by making them believe that they are helpless without Uncle Sugar coming in and providing for them a prescription each month for birth control because they cannot control their libido or their reproductive system without the help of the government" -- Paul said "if there was a war on women, I think they won."
"You know, I don't see so much that women are downtrodden; I see women rising up and doing great things," he said. "And, in fact, I worry about our young men sometimes because I think the women really are out-competing the men in our world."
Appearing on the same show, U.S. Senate Majority Whip Dick Durbin, D-Ill., said "what we saw with the budget agreement at the very end of last year and the beginning of this year is an indication of a new bipartisan spirit."
"This was an amazing breakthrough, we haven't done this for years," he said.
He said he hoped congressional Republicans do not try to extract concessions from Democrats in return for approving an increase in the federal debt ceiling when current borrowing authority expires.
"The president's position's clear: We should not play Russian roulette with America's economy," he said. "We shouldn't jeopardize its economic growth and kill off jobs because of another political squabble."