WASHINGTON — Conservatives on Capitol Hill are drawing a line in the sand: they will not vote to stop the government from shutting down if Obamacare is not defunded.

Led by Utah Republican Sen. Mike Lee, a dozen senators sent a letter Thursday saying they will not support any resolution to continue funding the federal government if President Obama’s health-care law remains funded.

Under current law, the government is funded until Sept. 30, meaning a continuing resolution needs to be passed to keep the government from shutting down.

“The Obama Administration’s recent decision to delay Obamacare’s employer mandate and eligibility verification for the individual exchanges is further proof the law is a failure that will inevitably hurt businesses, American families, and the economy,” Lee said.

“In light of this admission, I and several of my colleagues will be informing Sen. Reid that we will not vote for a continuing resolution that funds Obamacare,” he added.

Among those who signed onto the letter: Florida Sen. Marco Rubio, Texas Sen. Ted Cruz and Kentucky Sen. Rand Paul.

Over in the House, a large contingent of House Republicans are pushing a similar strategy, led by Rep. Mark Meadows of North Carolina.

“Congressman Meadows is leading a letter, currently co-signed by 66 Members, encouraging House leadership to defund Obamacare through the appropriations process,” spokeswoman Emily Miller told The Daily Caller on Thursday.

Meadows said she expects the movement to grow as lawmakers are “still signing on to support the effort.”

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