Washington (CNN) White House officials and a bipartisan group of senators are mounting an ambitious effort to push criminal justice legislation through Congress by the end of the year, four sources close to the process told CNN.

But first, Jared Kushner, President Donald Trump's son-in-law and senior adviser, who has been leading the White House's prison and sentencing overhaul push, must ensure the President is on board with the latest version of the measure. Kushner is slated to meet with Trump on Tuesday to press him to back the legislation, a senior administration official said.

The gears are also turning on Capitol Hill, where Senate Majority Leader Mitch McConnell, a Kentucky Republican, is expected to order a whip count later this week, with a promise to move the bill to the Senate floor if there are 60 votes supporting it, three sources familiar with the matter said.

The new legislation would:

Eliminate "stacking" provisions that result in offenders serving consecutive sentences for crimes committed using firearms.

Shorten mandatory minimum sentences, including reverting life imprisonment to a 25-year minimum for those convicted under the "three strikes" provision.

Expand the "drug safety valve" to reduce the number of nonviolent drug offenders receiving mandatory minimum sentences.

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