Republican Gov. John N. Dalton today sent the General Assembly a $13 billion two-year budget that is balanced through sharp cuts in state services and a modest 6.3 percent increase over the last budget.

Dalton told state legislators his budget reflected the "triple whammy" of Reaganomics, declining state revenues and recession. But the conservative Republican backed off recommending any tax increase to replace approximately $680.7 million in lost revenues, saying "any increase in taxes will be up to the members of this body and the next governor of Virginia."

That posture brought immediate criticism from Democratic supporters of Gov.-elect Charles S. Robb, who takes office this Saturday. "He ducked the issue," grumbled Del. Archibald A. Campbell (D-Wythe), chairman of the tax-writing House Finance Committee. "He should have said you'll have to increase taxes to carry out programs."

Under the Dalton budget, 73,000 state workers will go without a planned 4.5 percent salary increase this year, the Northern Virginia Metro system will receive a $7 million, or 33 percent, decrease in state construction funds and the state highway department will slip even further behind what officials say are its basic funding needs with a $347 million, or 16.1 percent, decrease from the last state budget.

Education, which already receives more than half of the state's general fund revenues, is in line for a $691 million increase, which accounts for most of the $807.5 million overall budget increase in the Dalton proposal.

The outgoing governor said at a press briefing earlier this week that he had attempted to shift state funds in "limited instances" to make up for $271 million in lost federal funds, mostly in the state's huge human resources agencies. Still, the impact of Reaganomics will be painful for the more than 300,000 state citizens who depend on programs such as Medicaid, Aid to Families with Dependent Children and forms of public assistance.

Despite grumblings against Dalton's plan, there were few indications today that the majority party would offer strong support for any efforts to regain lost federal revenues through state taxes in a year when all 100 House members must stand for reelection. There were, however, strong hints that some highway tax, perhaps a gasoline tax or higher user fees, will be considered.

"I think it's obvious to everyone that the highway problem is a special one that will have to be addressed separately if we want to see any highway construction," said Del. Richard Bagley (D-Hampton), chairman of the powerful House Appropriations Committee.

The state's highway department has been losing funds for years, largely the result of fuel-efficient cars that sharply have reduced the state's gasoline tax revenues, and highway officials now say that state highway construction and even minimal maintenance will come to a halt by 1986 if the trend is not reversed.

Dalton conceded that the funding decline spelled out in his budget could endanger more than $1.1 billion in federal highway matching funds to the state by 1988. But it was clear that he still carried deep wounds from his own failure two years ago to push through a highway gas tax increase.

"I leave that to your discretion," he told the assembly. "I think I've spoken to you enough on that, ladies and gentlemen."

Dalton's budget also included an expected one-third reduction in state funding for Metro construction costs in Northern Virginia, reducing the state's contribution from $21.7 million to $13.7 million. This already had produced an outcry from Northern Virginia's delegation that has threatened to withhold its votes from any gasoline tax proposal unless it guarantees increased funds for Metro.

Addressing the joint session of the legislature for almost 40 minutes, Dalton's speech brought applause from the Democratic-dominated assembly only once. Twice, the group rocked with laughter -- both times when Dalton informed them that he would not offer any advice on tax matters.

"The style and delivery was as usual -- Daltonian monotone," said Del. Clinton Miller (R-Shenandoah). "I assume it was good, but I didn't have my calculator with me."

In order to balance his administration's last budget Dalton told the legislators that he was recommending not only the suspension of a planned 4.5 percent salary increase for government employes, but also the reduction of maintenance funds for public buildings and a cut in capital building projects at state colleges and universities.

Education's two-year $5.5 billion budget represented a 14.3 percent increase over its previous allocation. Dalton stressed that state funding for higher education had moved from 15th place in the nation to 10th during his four years in office.

Reluctantly forced to postpone plans for one of two state prisons planned for 1985, Dalton also announced that the state will start doubling up prisoners at two new prisons opening this year to relieve the backlog of state inmates in local jails.

This brought criticism from some legislators. "I don't accept as settled law that they can put two people in one cell and call it constitutional," said Del. Theodore V. Morrison Jr (D-Newport News).

Robb, who will make his own budget presentation to the General Assembly next Monday, today reserved comment on the Dalton proposal. But two members of the Robb cabinet last week said they did not expect to see Robb recommend sweeping changes in the Dalton budget.

Legislators today said the state's budget problems -- particularly in the highway deparment -- will present Robb with the first test of his political leadership.

Sen. Edward E. Willey (D-Richmond), chairman of the Senate Finance Committee, launched the predicted debate over new taxes today with a proposal to redraw the Virginia's tax structure. Willey, one of the Senate's most influential members, also is expected to put forth a rescue plan for the troubled highway department.