RICHMOND -- Greater fear hath no politician than to give up a pet project.

But that is what several members of the Virginia General Assembly were moved to promise during last week's biennial capital budget tour, in which state agencies compete for construction funds.

"They sure made a good case," Sen. Clive L. DuVal 2d (D-Fairfax) said repeatedly, as he and other members of the legislature's money committee made firsthand inspections of universities, mental institutions and prisons during the four-day, 1,500-mile trip. The excursion will help determine what projects are funded in the 1988-90 budget, which comes before the legislature in January.

"You need {the support}, you've got it," pledged Del. Alson H. Smith Jr. (D-Winchester) after seeing conditions at several mental hospitals.

Smith, chairman of the House capital appropriations subcommittee, even volunteered to "give up money for my project" (a $1.5 million addition to Lord Fairfax Community College) if it is necessary to provide such basic needs as air conditioning, smoke alarms and other safety measures at the hospitals.

"There are no standards, no rules," said Sen. Joseph V. Gartlan Jr. (D-Fairfax), a member of the Senate Finance Committee, of the apples-and-oranges choices the budgetmakers face. "You just get a gut feeling."

What sounded like a perfectly reasonable request in one setting -- appeals by English and French professors at the University of Virginia for bigger offices -- paled a few hours later when the superintendent of the Central Virginia Training Center in Lynchburg sought air conditioning for a 30-patient ward of profoundly retarded children and adults.

Some decisions are easy, Gartlan said, such as "a building crumbling down in front of your eyes," which was the case in dormitories at predominantly black Virginia State University in Ettrick.

Gartlan said it would not be difficult to choose air conditioning at the DeJarnette Center, a 60-bed facility for emotionally disturbed children in Staunton, over the $16 million Project Explore, a recreation and theme park in Roanoke.

Senate Majority Leader Thomas W. Moss (D-Norfolk) derided the latter project as "Dickie World," in tribute to its most ardent backer, Del. C. Richard Cranwell (D-Vinton).

Gartlan said legislators "pick up tidbits" on the state tour that shed light on problems unrelated to the budget.

For example, he said, there is "the amazing notion that the lack of air conditioning at DeJarnette impairs the effectiveness of psychotropic drugs. That helps me to understand why the homeless, who certainly have no air conditioning, stop taking their medication."

Members of the money committees "understand that we have to represent everyone, think statewide," and set aside parochial concerns, said House Appropriations Committee Chairman Dorothy S. McDiarmid (D-Fairfax).

If her Fairfax constituents question why she votes for programs in Southwest Virginia, McDiarmid said, "I tell them the needs there are desperate. If we don't help them now, we'll be supporting them for the rest of their lives."

At many of the 23 stops on last week's tour, backers of a project sought a pledge from Gov. Gerald L. Baliles and the legislators that their proposal would be among those tapped.

But the governor had a standard answer for anyone who asked for a commitment: "We've got almost $1 billion {in requests} on our plate. It's clear we can't fund them all. We can't even see them all. But this is an important part of the process, and no decisions will be made until we have more time to study the proposals."

Traditionally, about 2 percent of the biennial budget is appropriated for capital expenditures, with about half of the total going go to colleges and universities, said Paul W. Timmreck, director of the department of planning and budget. In the current $20 billion budget, that translated to about $200 million.

There is a great deal of competition to get a project included on the tour, "but the sword can cut both ways," Timmreck said. "If you get there and see no compelling evidence, that hurts."

While most members of the tour contend that it is an integral part of the budget- making process, at least one participant whispered over the sounds of "On the Road Again" being played on the chartered bus that "this is not much more than a dog-and-pony show," especially in a year, such as this, when legislators face reelection Nov. 3.

Gartlan said he thought that this year's tour was better than past ones.

"Two years ago," he recalled, "we inspected a liquor store in Winchester, for God's sake. This one was more meaningful."