Senator Cory Booker of New Jersey on Wednesday unveiled a plan to tackle affordable housing that would provide a tax credit for renters to ensure they would not spend more than 30 percent of their income on rent — a sweeping new entitlement program that his campaign estimated would reach 57 million Americans, including 17 million children.

The plan, which draws heavily from legislation Mr. Booker introduced last year, comes about three weeks ahead of the first Democratic debate of the 2020 presidential race, as candidates jostle to introduce innovative policies that will help them stand out in a crowd of nearly two dozen. Mr. Booker, who has been talked about as a potential presidential contender since his days as mayor of Newark, has been stuck polling around 2 percent in most surveys.

Mr. Booker’s housing plan came as two other candidates rolled out new policy proposals Wednesday, former Representative Beto O’Rourke on voting and electoral issues and Senator Kirsten Gillibrand on marijuana legalization.

At the center of Mr. Booker’s housing plan is the renters’ tax credit, which would cover the difference between 30 percent of a person’s income and the fair-market rent in his or her neighborhood. There would not be an income cap limiting who could qualify, according to the campaign, which said the median participating family would receive $4,800 per year.