They are Majority Leader Eric CantorEric CantorEric Cantor offering advice to end ‘immigration wars’ Trump's olive branch differs from the golden eras of bipartisanship After divisive rally, Trump calls for unity MORE (Va.), Budget Committee Chairman Paul RyanPaul RyanThe Hill Interview: Budget Chair Black sticks around for now Gun proposal picks up GOP support GOP lawmaker Tim Murphy to retire at end of term MORE (Wis.), Appropriations Committee Chairman Hal Rogers (Ky.), Ways & Means Committee Chairman Dave Camp (Mich.), and Reps. John Carter (Texas), Ander Crenshaw (Fla.), Rodney FrelinghuysenRodney FrelinghuysenOvernight Finance: White House requests B for disaster relief | Ex-Equifax chief grilled over stock sales | House panel approves B for border wall | Tax plan puts swing-state Republicans in tough spot White House requests B for disaster relief Ryan: More hurricane aid likely coming in October MORE (N.J.) and Tom GravesTom GravesBillboard ads target Republicans who want to roll back net neutrality Week ahead: House eyes trillion-dollar omnibus | Crunch time for Senate ObamaCare repeal bill | Senate moves ahead on Trump nominees House GOP looks to advance trillion-dollar omnibus MORE (Ga.).

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In addition to requesting a conference, the resolution insists on the last House amendments to the continuing spending resolution. Those amendments would delay the individual health insurance mandate and end subsidies for insurance that senior officials would receive under the law.

The inclusion of that language on the healthcare law is what prevented the Senate from agreeing to it, and may be what keeps the House and Senate from finding a deal to end the shutdown.

Before the House even voted on the conference resolution, Senate Democrats said they would reject any request to talk about a spending resolution that contemplates undermining ObamaCare. The Senate adjourned until later Tuesday morning, when Democrats were expected to formally reject the House request to meet.

The rule was passed more than an hour after the Obama administration's Office of Management and Budget told agencies to execute their shutdown plans, which will furlough thousands of government workers, starting Tuesday.

Soon after the vote, the House adjourned until 10 a.m. Tuesday.