They are Majority Leader Eric CantorEric Ivan CantorThe Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Race for Republican Speaker rare chance to unify party for election Scalise allies upset over Ryan blindside on McCarthy endorsement MORE (Va.), Budget Committee Chairman Paul RyanPaul Davis RyanLaura Ingraham: George Will is ‘sad and petty’ for urging votes against GOP Seth Rogen: I told Paul Ryan I hate his policies in front of his kids George Will: Vote against GOP in midterms 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 Procter FrelinghuysenOvernight Health Care — Sponsored by PCMA — Dems see midterm advantage in new ObamaCare fight Lawmakers ask for increase in suicide prevention funding Overnight Defense: Trump defends summit results | GOP chairman tries to clarify canceled war games | House panel advances 4.6B defense bill | Saudis begin Yemen offensive MORE (N.J.) and Tom GravesJohn (Tom) Thomas GravesHouse committee approves spending bill that would boost IRS funding House panel advances financial services spending bill Georgia governor vetoes controversial hacking legislation 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.