Sen. Rand Paul (R-Ky.) on Thursday defended "Defund Obamacare" supporters in the Senate, who have come under criticism from House Republicans for suggesting they may not be able to stop a budget that includes funding for Obamacare.

Paul noted that even his 13-hour filibuster against the Obama administration's drone policies wasn't able to stop the Senate from approving the nomination of CIA director John Brennan.

"They have to realize that my filibuster delayed things for 13 hours, but didn't stop things," Paul said on Fox News.

Asked whether he would take part in a filibuster, Paul joked, "I don't know. But I better look for my better shoes. Last time, my feet hurt for two weeks."

Sen. Ted Cruz (R-Texas) said Thursday that he will filibuster against any budget that includes funding for the health-care overhaul law.

"I will do everything necessary and anything possible to defund Obamacare," Cruz said at a press conference.

Asked if that included a filibuster, Cruz said it did.

"Yes, and anything else, any procedural means necessary," Cruz said. "Listen, this is the most important fight in the country."

Cruz earlier Thursday appeared to suggest that the "Defund Obamacare" movement was doomed in the Senate because Republicans don't have the power to stop Majority Leader Harry Reid (D-Nev.) from stripping it from a budget bill -- something House Republicans, who will vote on Defund Obamacare on Friday, weren't all that happy about.

At this point, it seems clear that Senate Republicans don't have the votes to filibuster a bill that funds the health law. Several of the 46 GOP senators have expressed disagreement with the "Defund Obamacare" strategy, and Republicans would need 41 votes to filibuster.