As President Obama prepares to make the case Tuesday afternoon for overhauling the nation’s criminal justice system, bipartisan legislation in the House and initiatives on the state level have started to gain traction. But will that be enough to usher  a sweeping change in federal sentencing rules into law?

It depends on who you ask.

After holding nearly a year and a half of field hearings Reps. F. James Sensenbrenner (R-Wis.) and Bobby Scott (D-Va.) introduced the Safe, Accountable, Fair, and Effective (SAFE) Justice Act late last month, a comprehensive measure that would impose mandatory minimum sentences on higher-level drug traffickers rather than low-level offenders; apply life sentences for drug trafficking only in extreme cases; and allow eligible offenders to petition for re-sentencing under new trafficking laws.

The measure already has 30 co-sponsors, equally divided between Republicans and Democrats. Sensenbrenner said in an interview Monday that he has a simple strategy for ensuring House GOP leaders hold a vote of the bill: “Getting overwhelming bipartisan support. They can count votes as well as I can.”

The fact that several congressional Republicans in both chambers are engaged in the issue—including not just Sensenbrenner and several House colleagues but also Sens. Mike Lee (Utah), Rand Paul (Ky.) and Tim Scott (S.C.) — explains the White House’s cause for optimism. Asked Monday why the president believes reform of the nation’s criminal justice system is possible, White House press secretary Josh Earnest replied, “Well, to be blunt about it, because Republicans are indicating an openness to doing it.”

White House senior adviser Valerie Jarrett said in an interview Tuesday that the issue was personal to the president, who has met regularly with young people of color and has spoken of how they face a less forgiving environment than he experienced growing up.

"He just wants to make sure they don’t get unfairly stuck in the criminal justice system because they’ve made mistakes early in their lives, without the ability to ever have a second chance," she said.

She added that this week's events, which include the first-ever visit by a sitting president to a federal prison, "will put the spotlight on the issue, and remind America there are so many people who are incarcerated who we can’t afford to ignore."

Obama will both chronicle how the U.S. prison system has expanded since 1980, according to a senior official who asked not to be identified in advance of the president's speech, and what it has meant for American society.

While the president is not endorsing a specific bill to make it easier to strike a consensus, the aide added, he will outline several of the steps he thinks are essential for changing the way the country approaches crime, from preventative steps to incarceration. Obama will also speak about what he sees as the overuse of solitary confinement.

"He’s looking for common ground, and looking for ways of building as much consensus as possible," Jarrett said.

In recent months the president and his top aides have held a handful of private meetings aimed at laying the groundwork for a compromise bill on sentencing reform. In late February Obama brought 16 senators and House members to the White House to discuss general principles. And on April 16 Koch Industries' general counsel Mark Holden, who is working with officials from other foundations on the issue, met with Jarrett, White House domestic policy director Cecilia Muñoz and White House counsel Neil Eggleston on the issue.

But even as an alternative approach to crime-fighting gains momentum, not all Republicans — including Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa) — have shown quite the same openness to adopting some of the measures that most advocates see as part of a broad reform package. Grassley has been negotiating with Sen. Dick Durbin (D-Ill.) and a handful of other committee members for two months. On Monday, he said, “there are three or four items that have to be settled yet," without detailing the outstanding issues.

According to aides involved in the negotiations, lawmakers are likely to offer a bipartisan bill in the near future.

Several lawmakers and aides said they are eager for the president to specify what he would or would not accept in a sentencing bill,  to propel the discussion. Scott said in an interview that “it would be helpful” if the Justice Department endorsed the bill he and Sensenbrenner crafted, adding that since they solicited the department’s input during the hearing process, “we are hopeful that everybody’s going to singing off the same sheet of music.”

Advocates, for their part, said they were confident that recent action on the state level had many lawmakers from several states more comfortable with the idea of shifting away from the sort of criminal enforcement tactics that became popular in the late 1980s and early 90s. A coalition of liberal and conservative groups have coalesced around the need to cut the amount of spending on prisons and direct money instead to drug and alcohol treatment centers.

Marc Levin, who directs the Right on Crime initiative at the Texas Public Policy Foundation, noted that conservative states including Alabama, Georgia, Nebraska, South Carolina, Texas and Utah had adopted sentencing reforms in recent years. In January 2007, the Texas legislative budget board predicted that the state would have to spend “a few billion dollars” on providing 17,000 additional prison beds over the next five years, Levin said; later that year,  lawmakers approved $241 million on treatment services as well as drug courts and halfway houses.

Georgia has passed drug sentencing reforms for three sessions in a row, while California voters adopted a ballot proposition last fall making “non-serious, nonviolent crimes” misdemeanors instead of felonies unless the offender has specific previous convictions, and steers the money that will be saved by these changes and the re-sentencing of those now serving time toward mental health and drug treatment, education and victim compensation.

Lenore Anderson, who co-authored Proposition 47 and serves as  executive director of Californians for Safety and Justice, said voter attitudes had shifted decisively on the issue, and the goal of the proposition was that “we could finally put the nail in the coffin that the only way to talk about criminal justice was with a ‘tough on crime’ lens.”

Obama’s speech Tuesday, coming on the heels of his move to commute the sentences 46 non-violent drug offenders and visit Thursday to a federal prison, is likely to elevate the issue’s profile even further.

Some Republicans were not pleased at the president’s latest act of clemency. Sensenbrenner remarked: “I really am not really happy the president is engaged in a publicity stunt at the NAACP national convention, and pardoning a handful of drug offenders.”

Grassley, who has sparred with Obama over his executive actions on immigration and other matters, took advantage of the news to make a light jab at the president. "He's finally doing something that the Constitution allows him to do," he said. "That's quite an accomplishment."

Still, Levin noted that sentencing reform has proved so popular on the state level that Georgia Gov. Nathan Deal (R) sent out a direct-mail piece touting the connection between the legislative changes and the state’s reduced crime rate during the last election, while Ohio Gov. John Kasich (R) campaigned in African American churches on the issue.

“It’s exciting that good policy is turning out to be good politics as well,” he said. “We’ve established enough of a conservative beachhead on this, we’re not too afraid that just because the president’s for it, some people will say, ‘I can’t be for it.’ ”

Mike DeBonis and Sari Horwitz contributed to this report.