"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 AyotteThe Hill's Morning Report: Koch Network re-evaluating midterm strategy amid frustrations with GOP Audit finds US Defense Department wasted hundreds of millions of taxpayer dollars US sends A-10 squadron to Afghanistan for first time in three years 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 CoburnMr. President, let markets help save Medicare Pension insolvency crisis only grows as Congress sits on its hands Paul Ryan should realize that federal earmarks are the currency of cronyism MORE (Okla.), John CornynJohn CornynOvernight Finance: House panel to take up bill toughening review of foreign deals | Trump acknowledges Cohen payment on disclosure form | Officials set for new round of China trade talks Groups urge Senate panel to reject Trump's pick for Louisiana-based appeals court House panel will consider bill to boost foreign investment review powers next week MORE (Texas), Jim DeMint (S.C.), Mike EnziMichael (Mike) Bradley EnziSinger Jason Mraz: Too much political 'combat' in Washington Lobbying world Ethics watchdog calls for probe into Mulvaney over 'real estate dealings' MORE (Wyo.), Tim JohnsonTimothy (Tim) Peter JohnsonSenate GOP rejects Trump’s call to go big on gun legislation Court ruling could be game changer for Dems in Nevada Bank lobbyists counting down to Shelby’s exit MORE (S.D.), Rand PaulRandal (Rand) Howard PaulOvernight Defense: Senate confirms Haspel as CIA chief | Trump offers Kim 'protections' if he gives up nukes | Dem amendments target Trump military parade Hillicon Valley: Lawmakers target Chinese tech giants | Dems move to save top cyber post | Trump gets a new CIA chief | Ryan delays election security briefing | Twitter CEO meets lawmakers Overnight Finance: Watchdog weighs probe into handling of Cohen bank records | Immigration fight threatens farm bill | House panel rebukes Trump on ZTE | Trump raises doubts about trade deal with China MORE (Ky.), Jim RischJames (Jim) Elroy RischHouse passes bill to help small businesses guard against hackers Menendez admonished by Ethics panel, which says he broke the law GOP anxiety grows over Trump’s Iran decision MORE (Idaho), Marco RubioMarco Antonio RubioCongress — when considering women’s health, don’t forget about lung cancer Anti-Maduro Venezuelans not unlike anti-Castro Cubans of yore Tax reform postmortem reveals lethal dose of crony capitalism MORE (Fla.), Jeff SessionsJefferson (Jeff) Beauregard SessionsChris Christie compares Mueller investigation to 'Bridgegate' probe Oakland mayor fires back at Trump: ‘It’s my duty to protect my residents’ McCabe lawyer fires back at Trump: 'You need to stop lying’ MORE (Ala.), Pat Toomey (Pa.) and David VitterDavid Bruce VitterPlanned Parenthood targets judicial nominee over abortion comments Trump nominates wife of ex-Louisiana senator to be federal judge Where is due process in all the sexual harassment allegations? 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."