President Reagan won bipartisan support yesterday from 14 governors, including John N. Dalton of Virginia and Harry R. Hughes of Maryland, for massive cuts in federal spending, even though many of his proposals are likely to place additional burdens on state governments.

Hughes, one of eight Democrats invited to the briefing at the White House, said, "We all agreed, Democrats and Republicans alike, that something has to be done to turn the economy around. Obviously, when we learn what specific projects will be cut, there will be disagreement. But we begin in agreement."

"All we know," added Dalton, "is that military spending will be increased."

Dalton, whose state is heavily dependent on defense installations, said, "I agree that military preparedness should be at the top" of federal spending priorities.

"I just got my copy of the famous black book this morning, so I don't know where the cuts will be made," said Hughes after the two-hour visit. The governors were given lunch in the First Family's dining room, a sample of jelly beans and vague indications that their pet projects would be given consideration when the ax falls next week.

Hughes said he put in a plug for retaining substantial federal funding for two areas, transportation and urban development action grants.

"I mentioned transportation," said Hughes, who headed Maryland's department of transportation before resigning to run for governor, "because it is essential to what the president is trying to do in revitalizing the economy and reindustrialization."

Hughes cited the development grants as an example of a federal program "in which relatively few federal dollars generate large amounts of money in the private sector." Since 1978, Baltimore has received $44 million as seed money for projects include a Hyatt Regency hotel on the harbor, parking lots for a General Motors factory and renovation of a downtown theater.

Asked what Reagan's response was to his suggestions, Hughes shrugged. "He said, 'we're looking at that,'" Hughes said.

Virginia chief executive said he didn't make a pitch for any particular program, although he said he hopes that the entire 101-mile Metrorail system -- one vulnerable local project -- can be completed.

"But we all have our pet projects," Dalton said. Asked if Metro were one of his pets, Dalton hedged, saying only, "We don't have any specifics about what will be prepared."

Dalton, who is chairman of the Republican Governors Conference, refused to speculate about whether tax cuts currently working their way through the General Assembly in Richmond would be imperiled by the president's own plan for a 10 percent tax cut.

He said the president "is on the right track . . . in trying to get government under control" as a way to begin attacking inflation. "We want to give the private sector more control."

A recent report to Dalton showed that in fiscal 1977, Virginia got $1.7 billion, or about one-fourth of all its revenues, from the federal government, to administer more than 300 programs.

Dalton and Hughes said in separate interviews that federal funding could be reduced without substantially harming public services if the states are given more discretion in how to spend what federal money they do get.