When 10 big-city mayors, meeting that night at New York's Gracie Mansion, publicly deplored the lack of any urban program in the President's State of the Union message, they signalled that Jimmy Carter's great dilemma on domestic policy has intensified, not diminished, after one year in office.

President Carter has been seeking an innovative urban policy reducing the federal role. But the mayors and the federal bureaucracy want the same old programs - slicked up a bit with perhaps some cosmetics - at considerably higher levels of spending. Given that clash of intentions, submission of an urban plan has been postponed.

The same dilemma permeates most of Carter's domestic policy, accounting for the internal contradition of his State of the Union message. While avowing a neo-Jeffersonian ideal of limited government, it contains a neo-Rooseveltian agenda for big government.

This contradiction results less from indecision than frustration. Although Carter would clearly prefer to play Jefferson, the liberal-labor-minorities coalition that put him in office demands that he play Roosevelt. "This President's biggest problem is his constituency," one Cabinet member told us. But the preponderance of administration officials side with that constituency.

No issue exemplifies this situation better than the urban question. One urban plan prepared by the Department of Housing and Urban Development (HUD) was sent to the White House and then shipped back before the President saw it, with instructions to reduce proposed spending. Rewritten without dollar amounts, it was then rejected a second time.

The Carter White House is not one for clear articulation of internal disputes, but the President hinted at what was bothering him in a meeting with Office of Management and Budget (OMB) officials just before Christmas. His voice growing softer as he grew angrier, the President told the bureaucrats he will not consider dollar amounts until there is a clear program. That sent OMB and HUD technicians back to the drawing boards.

The President's intent became clearer when he received a staff memorandum from a Senate subcommittee recommending that "the President's urban policy should include powerful incentives for the states to become more involved in helping their cities." Carter bucked it over to HUD with the marginal note to "push this," as reported by the Jan. 14 National Journal.

But HUD is emotionally and intellectually incapable of "pushing" any plan to substitute local for federal power. HUD officials, both political and civil service, want existing federal programs that the President does not like. To HUD policymakers, there are two options for urban aid: present programs at existing dollar levels, or present programs at higher dollar levels.

The mayors fully agree. They deplore incentive schemes for state or local funding but want Carter to expand grant programs without more soul-searching. Thus the anger of the mayors watching the President over television at Gracie Mansion last Thursday night climaxes a year of growing irritation.

Conversely, Carter lately has been urged to reestablish his largely abandoned 1976 campaign theme by pressing for limited government - privately urged by some staffers, publicly urged by a few Carterite politicians, such as Rep. Elliott H. Levitas of Atlanta. Meeting with the President last Wednesday, Levitas was distressed to find 17 separate administration programs going before Congress this year.

So, Levitas was cheered by the State of the Union's playing down the role of government. "If he goes with the speech and forgets the 33 pages," Levitas added, "it will be good for him, good for us, good for the country."

That view may approximate public opinion but not the Democratic Party. The party's dominant liberal-labor faction views Carter's State of the Union language as either political rhetoric not to be taken seriously or as outrageous quasi-Republican posturing. That is also prevailing opinion within his own administration.

The President's inclination to appease this view while seeking new approaches has brought only frustration. Accordingly, he must soon choose between Elliott Levitas and his 1976 campaign theme on the one hand, or the mayors, big labor and minority pressure groups on the other. The eventual choice will reveal not only the final shape of his urban plan but also how strong a President Jimmy Carter can be.