WASHINGTON -- Sen. Mike Lee (R-Utah) conceded Sunday that the government will remain open despite a Republican threat to shut it down if Obamacare isn't defunded.

"We all know that the governments going to get funded," Lee said on "Fox News Sunday." "The question is whether the government gets funded with Obamacare or without it."

Lee has been spearheading an effort since Monday, with the support of about a dozen of his colleagues, under which Republicans would refuse to pass a continuing resolution that would keep the federal government open beyond Sept. 30 if it includes funding for the implementation of the Affordable Care Act.

The move is mostly an attention grab -- Senate Minority Leader Mitch McConnell (R-Ky.) refused to back it, and many other Republicans have rejected the idea. Lee, a leader in the tea party movement, acknowledged as much to host Chris Wallace, given that President Barack Obama would never sign a bill that unravels his signature health care law.

He nonetheless used the White House's decision to delay the law's employer mandate by a year as proof that it should go unfunded.

"If the president's not ready to implement the law, if it's not ready for prime time, Congress shouldn't fund it," Lee said.

Criticism of Lee's proposal mounted among his colleagues last week, with Sen. Richard Burr (R-N.C.) calling it the "dumbest idea" he'd ever heard of . A group of more than 60 House Republicans tried to push a similar effort via a letter to Speaker John Boehner (R-Ohio), but Rep. Peter King (R-N.Y.) on Sunday joined the ranks of GOP lawmakers to pour cold water on the idea.

"We should not be closing down the government under any circumstances. That doesn't work; it's wrong," King said during an appearance on CNN 's "State of the Union" with Candy Crowley." "And Obamacare passed ... We have to try to defund it. We have to try to find ways to repeal it, [but] the fact is we shouldn't be using it as a threat to shut down the government."

"I would put the debt ceiling in a different category," he added. "There's no reason to bring down the government. Let's make this work. Let's get the spending cuts we need. The American people get turned off with the threat of terror politics."