Aides said McConnell’s bill would target only the executive actions Obama announced in November, not an earlier directive from 2012 that provided protections to hundreds of thousands of immigrants brought illegally to the country as youths.

That could make it more difficult for the handful of moderate Democrats who opposed Obama’s executive actions when he announced them in November to vote against the legislation.

The move came as growing numbers of Senate Republicans called for Congress to jettison the immigration fight and pass a “clean” Homeland Security spending bill without immigration language. In wake of a federal court’s ruling last week stating that Obama had exceeded his authority and putting his immigration policies on hold, several Senate Republicans said the courts were the best place to fight that battle.

“Leave it to the courts. I think we have an excellent case before the Supreme Court,” Sen. John McCain, R-Ariz., said Monday night.