Two top Republican lawmakers on Sunday voiced optimism that the Senate can pass criminal justice reform.

Speaking on NBC’s “Meet the Press," Sen. Lindsey Graham, R-S.C., said he believes that there is enough bipartisan support to pass criminal justice reform legislation.

"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."

Graham was talking about the First Step Act, which President Trump enthusiastically threw his support behind on Wednesday.

[Opinion: Trump is right to embrace criminal justice reform]

House Speaker Paul Ryan, R-Wis., said the compromise legislation would be pushed through the House “this term” — even though Senate Majority Leader Mitch McConnell reportedly told Trump on Thursday there is not enough support to bring it up for a vote this year.

"The Republicans are the problem here, not the Democrats," Graham said. Graham, who is set to take over the Judiciary Committee next year, called the bill "the most important bipartisan piece of legislation in the Congress today."

Separately, on CBS’s “Face the Nation," Sen. Rand Paul, R-Ky., said he believes there is a “real chance” to pass the legislation.

“With President Trump being in favor of this criminal justice reform, he came out publicly for it, really it only depends on one senator now. If Sen. Mitch McConnell, from my home state, will allow a vote, it gets 65 to 70 votes in the Senate. It'll be one of the most popular things to ever pass,” Paul said.

Paul said getting a vote before the year’s end is all up to one person: McConnell.

“Sen. McConnell has the ability to call any vote he wants to anytime. He has promised in the past that he would allow this vote if there was popularity for it,” he explained.

When pushed by CBS’ Margaret Brennan on whether he knows McConnell will refuse to bring the legislation for a full vote, Paul said he hasn’t spoken to him about it yet.

“I haven't talked to him directly about it. The last time I talked to him about it, he said he was open to allowing a vote after the election,” Paul explained. “I really hope we can get a vote, but it's really up to Sen. McConnell. But it's very, very popular in Kentucky and very, very popular with people who support President Trump, so I hope he allows a vote.”

Bill provisions include shortening federal three-strike drug penalties from life in prison to 25 years, reducing two-strike drug penalties from 20 years to 15, allowing a firearm sentencing enhancement to run concurrently with the underlying penalty, and allowing retroactive sentencing for crack cocaine cases judged under tougher historical laws.

The Washington Examiner reported many of the bill's details earlier this month.