Alexandria Mayor Charles E. Beatley Jr. and the man seeking to replace him, Vice Mayor Robert L. Calhoun, disagreed last night in debate over city government spending in an era of federal and state funding cuts.

Speaking before the Old Town Civic Association, Democrat Beatley asserted that his Republican colleagues on the City Council were "famous for approving 3-hour parking limits" and then failing to appropriate money to pay for enforcement. The four-term incumbent mayor said Calhoun and the two other Republicans on the seven-member council voted against a budget item that provided for 11 new police officers in 1980.

Calhoun defended his vote while championing the Republican view. "That is true," he said of his vote. "It's also true that people who run government always want to hire more people."

So it went before an audience of about 75 at the Lyles Crouch Elementary School auditorium. Democrats defended city spending for social services and decried federal budget cuts, while Republicans downplayed party differences and declared that volunteerism and eliminating "fat and overhead" from city government could make up federal funding losses.

Beatley and Calhoun appeared along with the full slate of 14 council candidates--six Republicans, six Democrats and two independents--running in the May 4 election. All appeared last night in the latest of a round of appearances before civic associations. Calhoun, a two-term councilman, is the first Republican to run for mayor in at least 100 years. He has repeatedly attacked Beatley's governing style, criticizing it as lacking direction and drive.

The Old Town Civic Association tries to preserve historic downtown neighborhoods from high-rise, high-density development, and in past years its 200-plus members have crowded the candidate's meetings. Last night's crowd of about 75 included campaign workers.

"We tend to be exuberant to the extent of the problem of the moment," was how association member Andrea Dimond explained the turnout.

The six Democratic council candidates are incumbents Donald Casey and James Moran plus PTA activist Patsy Ticer, lawyer Mark Pestronk, accountant Lionel Hope and West End resident Richard Leibach.

The Republican council candidates are incumbents Carlyle C. Ring and Marlee Inman, as well as retired civil servant Richard Gardner, businesswoman Janet Wilson, consultant William Glasgow and lawyer Gene C. Lange.

The independents are former councilman Nicholas Colasanto, who is making a comeback attempt after his defeat in 1979, and swimming pool manager Bruce Adkins.