Republicans in the Senate took a step on Wednesday to avert a national crisis by voting to advance a bill to fund the Department of Homeland Security before its budget expires at the end of the week. Republicans in the House, however, intent on thwarting President Obama’s executive action on immigration, have been unwilling to back away from the dangerous impasse on this issue in their party.

If a budget for the department isn’t approved by the end of the week, there’s only one agency in the gargantuan bureaucracy where business would largely continue to operate as usual. It happens to be the United States Citizenship and Immigration Services, which processes visa, work permit and green card applications and is the very agency responsible for accepting petitions for deferred action from deportation that the Obama administration has offered to certain unauthorized immigrants.

Unlike other parts of the department, the citizenship and immigration services agency is financed almost entirely by applicant fees, rather than taxpayer dollars, making it immune to government shutdowns.

Republicans had warned that they would pass a bill to finance the Department of Homeland Security only if it included a provision blocking Mr. Obama’s initiatives, which would allow certain longtime immigrants to remain in this country and work lawfully but would not provide a pathway toward citizenship. The Senate majority leader, Mitch McConnell of Kentucky, agreed to untangle the two issues by putting forward a straight budget bill and vowing to introduce separate legislation that would stop the president’s program. Republicans in the House have not agreed to pass a similar bill.