Sen. Mike LeeMichael (Mike) Shumway LeeWhatever you think the Alabama special election means, you’re probably wrong How the effort to replace ObamaCare failed Overnight Regulation: Trump temporarily lifts Jones Act for Puerto Rico | Bill would exempt some banks from Dodd-Frank | Senators unveil driverless car bill MORE (R-Utah) said late Wednesday that his effort to block any funding resolution that includes money for implementing ObamaCare is gaining the support of his GOP Senate colleagues.

Sen. Pat RobertsCharles (Pat) Patrick RobertsThe Hill's Whip List: Republicans try again on ObamaCare repeal No. 2 Senate Republican backs McConnell in Trump fight Overnight Healthcare: McConnell warns Senate not to block repeal debate | Insurers knock Cruz proposal | WH tries to discredit CBO | Lawmakers propose .1B NIH funding boost MORE (R-Kan.) on Wednesday became the 14th senator to sign on to his letter to defund ObamaCare, Lee said.

Speaking at a town-hall meeting in Spanish Fork, Utah, Lee criticized the “blatant” and “unfair” characterization of his proposal as a shutdown threat. 

“What I’m trying to do is avoid a shutdown,” he said.

Lee described the Affordable Care Act as “unaffordable” and “fundamentally unfair.”

He also attacked President Obama for delaying the employer mandate and other ObamaCare provisions.

“He does not have the power to change the law after it’s been enacted,” Lee said.

Many GOP lawmakers in both chambers are pushing a move to block any funding measure that includes funding for the president’s signature healthcare reform bill. But some Republican lawmakers and strategists fear the move could result in a government shutdown, with voters holding the GOP responsible.

Earlier this week, former Sen. Jim DeMint (R-S.C.) urged voters to replace any Republican lawmaker unwilling to vote to defund ObamaCare during next month's budget showdown.

DeMint, the president of the Heritage Foundation, dismissed fears that Republicans would be blamed for a shutdown, as they were in the 1990s.

“The risk of that is so much less than the risk to our country if we implement ObamaCare, and so I’m not as interested in the political futures of folks who think they might lose a showdown with the president,” DeMint said Monday night at a town-hall meeting hosted by Heritage Action, the think tank's political arm, in Fayetteville, Ark.

Most House and Senate GOP leaders though have declined to sign on to the defunding strategy.