President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE spoke with Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) this week to urge him to move forward on a criminal justice reform package that has sparked internal divisions within the GOP.

During a Tuesday telephone call, Trump "did urge him to try to get this done in the lame duck," a senior White House official told The Hill.

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The conversation follows a White House meeting last week with Senate GOP leaders, during which McConnell told the president he did not believe there would be enough floor time to pass the measure in the lame-duck session.

Trump's lobbying effort comes as the criminal justice package faces an uncertain future and shows the president is willing to spend political capital to force action on it.

The bill has caused tension within the Republican Party, with Sen. Tom Cotton Tom Bryant CottonGOP brushes back charges of hypocrisy in Supreme Court fight Trump uses bin Laden raid to attack Biden Battle lines drawn on precedent in Supreme Court fight MORE (R-Ark.) ripping the measure and urging his colleagues to oppose it. Several top Senate Republicans, including Judiciary Committee Chairman Chuck Grassley Charles (Chuck) Ernest GrassleyThe Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy Read: Senate GOP's controversial Biden report MORE (Iowa), have said they support the measure.

McConnell's warning about the lame-duck calendar has the bill's advocates worried that he might quash it, despite backing from Trump and his son-in-law and senior adviser, Jared Kushner Jared Corey KushnerAbraham Accords: New hope for peace in Middle East Tenants in Kushner building file lawsuit alleging dangerous living conditions Trump hosts Israel, UAE, Bahrain for historic signing MORE.

The measure would reduce mandatory minimum sentences for certain nonviolent drug offenders and incentivize the use of anti-recidivism programs in federal prisons. Trump threw his support behind the bill last week at a White House event, saying "I'll be waiting with my pen" to sign it.

Supporters of the bill have raised further pressure on McConnell to bring it to the floor. Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) said Sunday on NBC's "Meet the Press" there is enough bipartisan support to pass it if McConnell allows a vote.

"Let’s start 2019 on a positive note," Graham said. "I’m urging Sen. McConnell to bring the bill to the floor of the Senate. It would get 80 votes. Mr. President, pick up the phone and push the Republican leadership."

Grassley echoed those sentiments on Sunday, tweeting: "I join my colleagues Sen. Graham & Paul calling on Ldr McConnell to bring criminal justice reform to the floor for a vote this yr It’s the right thing to do 4our country Bipartisan support & we have the votes to pass it Tough on crime but FAIR #PassFirstStep"

McConnell, however, is viewed as wanting to avoid stoking tensions between the bill's supporters and opponents, such as Cotton. Sen. Mike Lee Michael (Mike) Shumway LeeMcConnell shores up GOP support for coronavirus package McConnell tries to unify GOP Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (R-Utah), a supporter of the bill, accused Cotton of spreading "fake news" about the bill during a Twitter spat, which some saw as a possible prelude to a nasty floor battle.

Cotton had said the bill would grant prisoners an "early release," a claim Lee denied.

The Senate leader has said publicly he would whip support for the bill when senators return to Washington after their Thanksgiving break. If he determines it has sufficient support, then he will weigh it against other lame-duck priorities like nominations, the farm bill and a government funding measure.