In a year of tight budget constraints, President Carter has recommended more spending for education, jobs, housing and the cities - traditional concerns of the Democratic Party and its voters.

His budget proposals - representing tough political and fiscal tradeoffs - were generally welcomed by the major elements of the Democratic coalition. But those speaking for the minorities, the poor and the cities left no doubt they would continue to press the president for more.

"The president is moving in the right direction," said the Rev. Jesse Jackson, who heads Operation PUSH, a Chicago-based organization that stresses economic and educational needs of the poor. "But what he offers is too little and too slow."

Jackson said Carter's budget "does not represent the kind of commitment to revive the cities that he has put forth to conserve energy or to reorganize the government. The dosage of medicine has to be in proportion to the depth of the sickness."

Seeking to cut the share of the national wealth consumed by the government and to make room for a $24.5 billion net tax cut for economic stimulus, Carter proposed spending only $7.8 billion more in fiscal 1979 than would be spent "if we simply left the federal government on automatic pilot."

That Carter-ordered increase in the "current-services" budget is less than 2 percent of the $500 billion budget.

But within that constraint, he managed to increase budgeted outlays from this year to next:

Over $800 million, or 14 percent, for elementary, secondary and vocational education.

Almost $2 billion, or 17 percent, for public service jobs and job-training.

Nearly $1 billion, or 11 percent, for housing and community improvement.

Overall, the budget documents said, there is a $2.6 billion, or 19 per cent increase in direct federal assistance for urban regions. The figure includes housing, jobs, transportation and economic development.

Along with energy, the environment and basic scientific research, these areas represent what administration officials called the president's "personal priorities" for non-defense spending. One of Carter's budget aides noted that almost all these increases were discretionary - not required by law.

Nonetheless, there were complaints from some public officials and interest-group leaders that the administration was being stingy.

Rep. Henry S. Reuss (D-Wis.), chairman of the House Banking Committee and its subcommittee on the cities, said "the cities have little cause for rejoicing. They would have been better served by more direct job creation, rather than through tax cuts."

Govs. William G. Milliken (R) of Michigan and Milton J. Shapp (D) of Pennsylvainia, in a statement issued on behalf of their fellow state executives, acknowledged that, "on the whole, the budget does not cut growth in programs where state and local governments would be forced to make up the difference out of their own funds."

But, citing several specific omissions, they said "it does not provide any new dollars that could be used to meet needs deferred during the recession."

Despite these critical comments, several groups interested in urban programs expressed praise for the Carter budget.

Their reaction was probably heightened by weeks of reports that Housing and Urban Development Secretary Patricia Roberts Harris was locked in struggle with the Office of Management and Budget.

As it turned out, the HUD budget is up $1 billion, Sen. William Proxmire (D-Wis.), chairman of the Banking, Housing and Urban Affairs Committee, praised Carter for proposing to increase new construction starts in federally assisted housing from 238,000 units this year to 331,000 in fiscal 1979.

"New construction in the long run is vital for helping low-income people have better housing and for improving the general environment of the cities," he said.

Alan Beals, executive director of the National League of Cities, said the HUD budget "looks quite good." But, along with others, he said he was concerned about the budget's vagueness on additional funds to finance the urban initiative the president has promised to submit in March.

Administration officials said that a substantial part of that initative was reflected in the increased funds for jobs, schools, mass transit and economic development in urban areas. They also said the president's contingent fund was expanded to $3 billion to provide some leeway for the unspecified urban programs. And they left open the possibility, if he decides to recommend more spending than that for the cities in fiscal 1979, of going back to Congress with a supplemental appropriations request.

At the same time, administration officials called attention to sections of the budget showing that states and local governments, as a group, are enjoying budget surpluses, while the federal government is running $60 billion in the red.

A table showed that the operating accounts of the "state and local sector" moved from deficits in the recession years of 1974 and 1975 to a $3.9 billion surplus in 1976.

Data for the first nine months of 1977 showed those governments accumulating a $12 billion surplus, the highest since the mid-1940s.

Administration officials also noted that federal grants in aid reached $80 billion this year and are scheduled to rise to $85 billion next year. These now provide more than one-fourth of the budgets for state and local governments.

However, they acknowledge that surpluses are not equally distributed and that some of the big cities still face severe fiscal problems.

As John Shannon, the assistant director of the Advisory Commission on Intergovernmental Relations, put it, "A billion-dollar Texas surplus doesn't do the mayor of Buffalo much good."