Homelessness and hunger are tightening their grip on American cities, while public tolerance of those in distress may be declining, the United States Conference of Mayors said.

"This year's report is especially troubling," Charlotte, N.C., Mayor Sue Myrick, co-chairwoman of the conference's Task Force on Hunger and Homelessness, said in a statement."Our past failures to solve poverty and hunger and homelessness are catching up with us, and many people are becoming less tolerant of the situation, less patient with the people on the streets," she said.

Two-thirds of the 30 cities polled in the annual survey said public attitudes toward the needy had turned negative or were mixed.

"The NIMBY (not in my back yard) attitude is prevalent," officials in Phoenix reported.

"A severe anti-homeless backlash has increased dramatically in the past year" due to violence, aggressive panhandling and misuse of parks involving the homeless, said Santa Monica, Calif., officials.

Almost all the cities surveyed said expanding programs to feed and shelter those in need fell short of growing demand. Cities saw little hope for relief as the nation slid into recession, meaning more jobless and homeless and dwindling public funds to help them.

Requests for food aid were up 22 percent in 1990, while demand for emergency shelter increased by 24 percent, the survey found.

Meanwhile, emergency food resources were up only 4 percent, and available shelter beds increased by 3 percent.

Officials in 45 percent of the cities said their emergency facilities have inadequate food supplies. Demands for food went unmet 14 percent of the time. Cleveland was unable to meet 50 percent of demand, Los Angeles 30 percent and Nashville 25 percent.

Shelters in 70 percent of the cities must turn away homeless families because of lack of resources. On average, 19 percent of requests by homeless people for emergency shelter were unmet. Those included 70 percent in Phoenix, 56 percent in San Juan, Puerto Rico; and 50 percent in Alexandria, Va., and Charlotte.

Requests for food were up in 24 cities, led by a 94 percent jump in San Juan, 50 percent in Providence and 40 percent in Boston.

Every city said demand for food aid will go up in 1991.