"I don't know if the party has to have a leader," Blunt told Bob Schieffer Friday on Washington Unplugged, CBSNews.com's weekly political Web show. "I think it's more important Republicans get back to talking about how we solve problems."
As Republican National Committee Chairman Michael Steele continues to come under scrutiny from his fellow Republicans, the party has been grappling for ways to overcome its lack of strong leadership and its slipping popularity among Americans.
Blunt, who is running to fill the Missouri Senate seat being vacated by Republican Kit Bond in 2010, told Schieffer that the Republican party cannot let Democrats set the agenda for issues like health care, energy policy, or tax policy.
"It's very important for Republicans to talk about what our alternatives would be," he said. "We have to really effectively look for ways to advance what we're for in health care, in energy, in how to create jobs and help families."
More than two thirds of Americans approved of President Obama at the end of his first 100 days in office, but Blunt said the president's policies are not as popular as he is.
"I don't believe the American people have had a chance yet to zero in on the things he's trying to advance," he said.
You can watch the full show below, which begins with the interview with Blunt. Also included is an interview with actress Goldie Hawn and a roundtable discussion on Pakistan with CBS News' chief foreign affairs correspondent Lara Logan and national security consultant Juan Zarate.