Democrats have pushed hard to label Limbaugh, a very popular conservative talk radio host, a voice for the Republican party after he made controversial remarks about a Georgetown University law student who testified for a Democratic hearing. Over the span of three days, Limbaugh called Sandra Fluke a “slut” and a “prostitute,” among other remarks, for supporting the administration's new insurance mandate for employers to provide contraception without charging a co-pay. Limbaugh issued an apology for the controversial remarks over the weekend, but his critics are not satisfied.

Cohen and other Democrats have urged advertisers to drop sponsorship of Limbaugh’s show since the controversy began, and Cohen announced on the House floor Tuesday that he would no longer run ads with Clear Channel Communications unless they drop Limbaugh from their lineup.

Romney addressed the issue briefly when asked about it on the campaign trail in Ohio earlier this week. "It's not the language I would have used," Romney said. He went on to add that he is "focusing on the issues I think are significant in the country today” and declined to weigh in again when asked on Tuesday in Massachusetts.

Cohen and the Obama campaign both criticized Romney for not wading further into the controversy.

"What Mitt Romney said was so Mickey Mouse," Cohen said. "Romney's got lots of problems and Limbaugh is one. He won't stand up to the bully."

Top Obama campaign strategist David Axelrod also suggested Romney "took a pass" on criticizing Limbaugh's remarks.

"I thought that was a cowardly answer and it was a test of leadership, and one that he failed," Axelrod told CNN's Anderson Cooper earlier this week.

The Romney campaign did not immediately respond when asked to comment.