Leaders of the National League of Cities went to the White House yesterday to tell President Reagan about the effects of budget cuts, recession and layoffs on their cities. Reagan responded with a story about a man who drew Social Security disability benefits while he continued to work.

"He seems to me to continue along with analysis by anecdote," Mayor George Latimer of St. Paul, Minn., a Democrat, said with an air of annoyance, "but his anecdotes are not my anecdotes." Latimer said the stories that stick in his mind are of the 5,200 job seekers who lined up at a new department store in St. Paul the other day and of 2,000 others who vied for 200 jobs for the hard-core unemployed.

A year ago the League of Cities, whose members are the mayors and council members of big cities, suburban towns and rural hamlets across the nation, had enthusiastically endorsed Reagan's economic recovery program. But at their annual winter meeting here Sunday and yesterday, they made it clear that their support had evaporated.

"The combination of tax cuts, increases in defense spending, continued rapid growth of entitlement programs and high interest rates is driving the federal budget deficit and the total national debt to dangerous levels," a formal resolution adopted by the league's executive committee said.

The group urged a moratorium on cuts in federal grants-in-aid to state and local governments and also asked Reagan to adopt a less restrictive monetary policy, to delay the 1983 tax cut and to curb the growth of spending on retirement programs and defense in order to reduce the deficit.

During their 45-minute meeting, the league's leaders said, Reagan expressed support for curbing the growth in cost of retirement programs, was "extremely rigid" about his defense budget and did not respond to their request for a moratorium on cuts in social programs beyond reciting the anecdote about the man on disability benefits.

League leaders said they intend to concentrate their efforts on Congress.

Later yesterday, Vice President Bush urged the group's support of the president's federalism proposal. The league's executive committee deferred action on federalism until mid-May.

Bush said he knew that cuts proposed in the next fiscal year's budget would not be painless. "You're going to have to make some very tough decisions, just like we had to make some very tough decisions in the budgetary process," he said.

But Indianapolis Mayor William Hudnut, a Republican, said after the vice president's speech that he thought patience in the industrial North was beginning to wear thin.

"The American people are geared to a nine-inning mentality as it is," Hudnut said. "They've been giving it 15 months now, roughly speaking. . . . You cannot ask them to go on forever waiting for the economy to turn the corner."