Conservative senators are threatening to shut down the government unless the implementation of Obamacare is halted.

Having railed against the Affordable Care Act (ACA) since before it passed, a group of Senate conservatives will take their fight to a new level, publicly refusing to fund the federal government if the ACA's implementation continues.

Sen. Mike Lee (R-Utah) will unveil a letter on Thursday, signed by an undisclosed number of colleagues, promising to vote down the next continuing resolution if it funds ACA implementation. The current funding measure runs out Sept. 30. Unless Congress passes a new funding measure by that date, the government will shut down.

"If the administration will not enforce the law as written, then the American people should not be forced to fund it," the letter says, referring to the Obama administration's delay of the ACA's mandate that businesses provide coverage for employees. Lee will unveil the list of signers Thursday.

Sens. James Inhofe, R-Okla., Marco Rubio, R-Fla., and John Thune, R-S.D., have signed on, their offices have confirmed to ABC News.

Senate Minority Leader Mitch McConnell (R-Ky.) has supported repealing the ACA, but he is not backing Lee's letter and he's under some pressure from the right to do so.

"I think our main goal going into the year-end discussion is to not walk away from the bipartisan agreement that we made two years ago to reduce spending," McConnell told reporters Tuesday. "My view is that we should do what we promised two years ago, and that'll be my goal going into the final discussions."

Today, the Club for Growth publicly urged McConnell to sign on.

"If Senator McConnell is committed to defunding ObamaCare, then he should sign the Lee letter and promise not to support a continuing resolution or any budget that funds ObamaCare," Club for Growth President Chris Chocola said in a press release. "We are disappointed by rumors that Senate Republican leadership is pressuring senators not to sign Lee's letter or to remove their names - they should instead encourage others to sign on."

McConnell has backed a bill by Sen. Ted Cruz, R-Texas, to repeal the ACA.

Government-shutdown threats could become a headache for House Speaker John Boehner, as continuing resolutions typically originate in the House. Boehner and McConnell have been at the center of spending and debt negotiations with the White House during President Obama's tenure.

Here's the letter:

Dear Leader Reid:

We view the Obama Administration's recent decision to delay Obamacare's employer mandate and eligibility verification for the individual exchanges as further proof the law is a failure that will inevitably hurt businesses, American families, and the economy.

In light of this admission, we believe the only way to avert disaster is to fully repeal Obamacare and start over with a more sensible, practical approach to reforming our healthcare system.

However, if Democrats will not agree with Republicans that Obamacare must be repealed, perhaps they can at least agree with the president that the law cannot be implemented as written. If the administration will not enforce the law as written, then the American people should not be forced to fund it.

This is a matter not only of fiscal prudence, but of fundamental fairness as well. The president cannot seriously expect to waive Obamacare's onerous mandates on large businesses, while simultaneously forcing individuals and families to pay to implement an individual mandate the public has opposed since before the law was even passed.

For these reasons, we will not support any continuing resolution or appropriations legislation that funds further implementation or enforcement of Obamacare.

Sincerely,