"We want to ensure adequate review of all legislation so that we may support final passage in a prompt manner," the committee wrote.

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The letter says senators should clear bills they want passed this year with the Steering Committee before the deadline. "We will regrettably be unable to grant our consent for items submitted after this date," the letter states.

It was signed by Sens. Kelly AyotteKelly Ann AyotteUS sends A-10 squadron to Afghanistan for first time in three years No, the US did not spend million on a gas station in Afghanistan Lessons from Alabama: GOP, throw out the old playbook MORE (N.H.), Saxby ChamblissClarence (Saxby) Saxby ChamblissLobbying World Former GOP senator: Let Dems engage on healthcare bill OPINION: Left-wing politics will be the demise of the Democratic Party MORE (Ga.), Tom CoburnThomas (Tom) Allen CoburnPaul Ryan should realize that federal earmarks are the currency of cronyism Republicans in Congress shouldn't try to bring back earmarks Republicans should know reviving earmarks is a political nightmare MORE (Okla.), John CornynJohn CornynSenate faces difficult path to immigration deal Emboldened conservatives press Ryan to bring hard-right immigration bill to floor Gorsuch has dinner at GOP senator’s home MORE (Texas), Jim DeMint (S.C.), Mike EnziMichael (Mike) Bradley EnziGOP is addressing tax cuts and a pension bill that could help coal miners Overnight Finance: Congress sends Trump funding bill to avert shutdown | WH sees 'tentative' deal on defense spending | GOP discovers corporate tax snag | Consumer bureau fight heats up | Apple could see B windfall from tax bill Overnight Finance: Congress sends Trump bill to avert shutdown | GOP discovers corporate tax snag | CFPB leadership battle rages MORE (Wyo.), Tim JohnsonTimothy (Tim) Peter JohnsonCourt ruling could be game changer for Dems in Nevada Bank lobbyists counting down to Shelby’s exit Former GOP senator endorses Clinton after Orlando shooting MORE (S.D.), Rand PaulRandal (Rand) Howard PaulOvernight Regulation: Trump’s former chemical safety nominee leaving EPA | Senate confirms Powell as Fed chair | NTSB 'gathering information' on Tesla crash Overnight Finance: Senate confirms Powell as Fed chair | Mulvaney declares 'new mission' for consumer bureau | Trump says solar tariffs will boost jobs Senate confirms Jerome Powell as Fed chairman MORE (Ky.), Jim RischJames (Jim) Elroy RischGovernment needs to help small businesses follow regulations McConnell works to salvage tax bill The Hill's Whip List: Where Republicans stand on Senate tax bill MORE (Idaho), Marco RubioMarco Antonio RubioOvernight Regulation: Trump’s former chemical safety nominee leaving EPA | Senate confirms Powell as Fed chair | NTSB 'gathering information' on Tesla crash Overnight Cybersecurity: Mueller interviewed Sessions in Russia probe | Comey met investigators last year | Dems demand social media firms probe Russian bots | Missing FBI text messages anger Republicans Overnight Finance: Senate confirms Powell as Fed chair | Mulvaney declares 'new mission' for consumer bureau | Trump says solar tariffs will boost jobs MORE (Fla.), Jeff SessionsJefferson (Jeff) Beauregard SessionsTrump appears to call out Samsung over missing FBI text messages Sessions: Trump following through on promise to lower crime Stakes intensify: Mueller seeks to question Trump MORE (Ala.), Pat Toomey (Pa.) and David VitterDavid Bruce VitterTrump nominates wife of ex-Louisiana senator to be federal judge Where is due process in all the sexual harassment allegations? Not the Senate's job to second-guess Alabama voters MORE (La.).

Recently, Senate Republicans have been increasingly wary that the Obama administration and House Republican leaders are working on a deal to avoid the fiscal cliff that some senators may not support. While a deal on taxes and spending is unlikely to be hotlined, the GOP deadline is generally meant to make it less likely that any surprise or objectionable legislation can be rammed quickly through the Senate.

On Thursday, Sessions, the Senate Budget Committee ranking member, demanded that the fiscal-cliff talks be held in the open because keeping them secret gives President Obama an advantage.

"All this secrecy allows the president to position himself by saying he's for a balanced plan," Sessions said. "This process needs to be taken out of the shadows."