They are Majority Leader Eric CantorEric Ivan CantorConservative House Republican welcomes Clark as chief of US Chamber Former House GOP leader: Fear of telling 'truth' to voters led to Capitol riot Biden faces tall order in uniting polarized nation MORE (Va.), Budget Committee Chairman Paul RyanPaul Davis RyanCPAC, all-in for Trump, is not what it used to be Cruz hires Trump campaign press aide as communications director Bottom line 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 FrelinghuysenBottom line Republican lobbying firms riding high despite uncertainty of 2020 race Ex-Rep. Frelinghuysen joins law and lobby firm MORE (N.J.) and Tom GravesJohn (Tom) Thomas GravesGreene's future on House committees in limbo after GOP meeting McConnell says Taylor Greene's embrace of conspiracy theories a 'cancer' GOP has growing Marjorie Taylor Greene problem 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.