The Senate moved closer Tuesday to a deal to avert a partial shutdown of the Department of Homeland Security, but the proposal faced an uncertain future in the House, where Republican leaders conspicuously refused to embrace it.

Senate Majority Leader Mitch McConnell (R-Ky.) told reporters he was prepared to move swiftly to extend funding for DHS through the fiscal year in a bill that is not contingent on Republican demands to repeal President Obama’s executive actions on immigration.

Under McConnell’s proposal, the Senate would vote first on the funding measure and then hold a separate vote on a bill to undo Obama’s new immigration initiatives. McConnell hopes to assuage conservatives who are determined to confront the president on what they see as abuse of his executive authority.