WASHINGTON -- Sen. Ted Cruz (R-Texas) isn't exactly winning over his Republican colleagues by pressing them to vote against bringing up a bill to defund Obamacare.

Cruz is urging Senate Republicans to filibuster a House-passed bill this week that would do two things: fund the government past Oct. 1 and defund President Obama's health care law. Since Democrats control the Senate, and since they've already vowed to strip out the Obamacare provision and only hold a clean vote on funding the government, Cruz says Republicans should vote against bringing up the bill at all -- and be willing to risk a government shutdown. On top of that, Cruz said Sunday that anyone who votes to bring up the bill is, in effect, voting for Obamacare.

Sen. Lindsey Graham (R-S.C.) said Monday that Cruz's approach is all wrong, both procedurally and politically.

"Why would you filibuster a bill you like?" Graham asked, during a Fox News Radio interview. "I don't think it would be smart of the Senate to shut down the government if we don't get [Democrats] to bend to our will before we take the vote."

Graham, who noted that he's voted against Obamacare for years, said he has a better and more "responsible" strategy that hands Republicans a win, without risking a shutdown: Let Democrats go ahead and strip out the provision defunding the health law, which forces them to "own every aspect of that funding," while Republicans can show their distaste for Obamacare by voting to keep the defunding provision.

"The more we can make [Democrats] own this bill over time, the easier it is for us to basically replace it," Graham said.

Cruz, a tea party favorite thought to be eyeing a 2016 presidential run, was showing early signs of his filibuster plans on Monday. He emerged on the Senate floor to object to an unrelated effort by Senate Majority Leader Harry Reid (D-Nev.) to move into debate in order to confirm a handful of judicial nominees -- nominees that leaders in both parties had already agreed to confirm. Cruz relented after a few minutes, but came back later and requested that the Senate just pass the House-passed funding bill, as is. Reid predictably objected.

During his Fox News Radio interview, Graham said he's "not upset with Ted" for his tactics but said that he, too, has an opinion: that Republicans need to be smart about winning over the public and picking up more seats in 2014. He cited polls showing little public support for a shutdown, even among those who don't like the Affordable Care Act.

"It's the highest risk for Republicans with the least amount of return," Graham said. "I want my party to reemerge as the majority party and I want to win the White House. Shutting down the government takes attention away from the flaws of Obamacare, and it's not the best tactic."

Cruz said last week that it wouldn't be "the end of the world" if the government shuts down while Republicans wage war over Obamacare. But a number of Senate Republicans say they're not willing to risk it for a losing battle over the health law, given that Democrats control both the Senate and the White House. Sen. Richard Burr (R-N.C.) called it "the dumbest idea I've ever heard," and on Sunday, Sen. Tom Coburn (R-Okla.) said anyone taking Cruz's approach isn't facing "political reality."

"Tactics and strategies ought to be based on what the real world is, and we do not have the political power to do this," Coburn said on CBS' "Face the Nation."

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