WASHINGTON — The country is in the grips of an escalating housing affordability crisis. Millions of low-income Americans are paying 70 percent or more of their incomes for shelter, while rents continue to rise and construction of affordable rental apartments lags far behind the need.

The Trump administration’s main policy response, unveiled this spring by Ben Carson, the secretary of housing and urban development: a plan to triple rents for about 712,000 of the poorest tenants receiving federal housing aid and to loosen the cap on rents on 4.5 million households enrolled in federal voucher and public housing programs nationwide, with the goal of moving longtime tenants out of the system to make way for new ones.

As city and state officials and members of both parties clamor for the federal government to help, Mr. Carson has privately told aides that he views the shortage of affordable housing as regrettable, but as essentially a local problem.

A former presidential candidate who said last year that he did not want to give recipients of federal aid “a comfortable setting that would make somebody want to say, ‘I’ll just stay here; they will take care of me,’” he has made it a priority to reduce, rather than expand, assistance to the poor, to break what he sees as a cycle of dependency.