But for Mr. Kushner, it was a rare success after perhaps the most difficult period he has faced as a member of the Trump family and as a high-ranking official in the Trump White House.

His close relationship with Prince Mohammed bin Salman of Saudi Arabia, whom he has defended even after intelligence agencies concluded that the prince ordered the killing of Jamal Khashoggi, the Saudi journalist, has generated bitter criticism from even Republicans. Within the White House, where Mr. Kushner has feuded with John F. Kelly, the chief of staff and technically his superior, his attempt to replace him with Nick Ayers, an ally, backfired when Mr. Ayers would not agree to Mr. Trump’s conditions for the job.

And other issues on which Mr. Kushner has focused have gotten little traction. The release of his Middle East peace plan has been delayed until next year, and some of the top people on his team tasked with innovating the government have already left the Trump administration.

But criminal justice is something personal. Mr. Kushner’s father, after being sentenced in 2005, served 14 months in an Alabama federal prison for tax evasion, witness tampering and making illegal donations.

“Jared is committed in a way you can only be when you’ve seen your daddy hurt,” said Van Jones, a liberal CNN host who has worked closely with Mr. Kushner on the issue. “What I’ve seen is someone who is personally driven to make a powerful change in the experience of people behind bars.”

Senator Charles E. Grassley of Iowa, the chairman of the Senate Judiciary Committee, who had been part of the coalition that pushed a more extensive criminal justice bill during the Obama administration, first approached Mr. Kushner about the issue in the opening months of the administration last year and asked him to meet on the issue.