WASHINGTON — In the past three years, Senator Charles E. Grassley, chairman of the Judiciary Committee, blocked a Democratic Supreme Court nominee for more than a year, pushed through an army of conservative judges and helped cement a conservative Supreme Court by securing confirmation of the most controversial high court nominee in a generation.

All of that has come at great personal cost, so the 85-year-old Iowan had some chits to call in when on Monday morning, he joined a private phone call with Senator Mitch McConnell of Kentucky, the majority leader, to discuss a bipartisan breakthrough to overhaul the criminal justice system and the nation’s sentencing rules.

I have been there for you, Mr. Grassley told Mr. McConnell, the man standing in the way of a quick vote on the measure. And I would hope this is something that you would help me make happen, he said, according to three people familiar with the call who were not authorized to publicly discuss the conversation.

The direct lobbying by Mr. Grassley was just part of a pressure campaign aimed squarely at Mr. McConnell this week as an unusual coalition of senators, conservative advocacy groups and White House officials press to change the nation’s sentencing and prison laws. With President Trump supportive of the effort and Speaker Paul D. Ryan pledging to move it through the House, they increasingly view the Senate majority leader as the lone obstacle to unwinding some of the federal tough-on-crime policies of the 1980s and 1990s.