For years, the Democrats who dominate Virginia's General Assembly have said they need only one thing to guarantee harmony in the state capitol: a Democratic governor.

They got their wish with the victory of Gov.-elect Charles S. Robb, yet statehouse leaders are now predicting next January's legislative session will be the most fractious and partisan they've seen in years. The reasons:

* A startling string of Republican victories in the House this week has significantly eroded the Democratic majority, giving GOP members the tools to block some Democrat-sponsored legislation.

* Democrats, worried over GOP gains, are threatening to redraw the House of Delegates's electoral districts to guarantee protection of the dwindling Democratic majority.

* An expected budget shortfall of $1 billion or more as a result of Reagan budget cuts will pit Democrat against Democrat, Republican against Republican, in a scramble to protect hometown programs.

* The overwhelming election defeat of GOP lieutenant governor candidate Nathan H. Miller, who was accused of using his state Senate seat to benefit his law firm's clients, is sure to spark new debate over the state's toothless conflict of interest laws. Many legislators see his defeat as a mandate for tougher ethics laws, but some key Democratic leaders, who have themselves been accused of conflict, are likely to resist strenuously.

Overall, this week's statehouse elections brought Republicans 33 seats in the House of Delegates -- an increase of eight seats over last year, and a bigger GOP delegation than the party has claimed in Virginia since Reconstruction.

"I don't think there's any question that the House will be more partisan," said House majority leader Thomas Moss (D-Norfolk), who promised that Democrats will be tougher at redistricting the state to maximize the Democratic advantage. A federal court declared the first redistricting plan unconstitutional and ordered the legislature to redraw its House districts.

"We've been criticized in the past for not being partisan enough," Moss said. "If we can be a little more partisan and protect ourselves more, we should."

Despite their new-found voting strength in the House, Republicans are in no way assured of more clout when the legislature convenes in January. With the loss of the governor's office and the surprise defeat of House Republican leader Jerry Geisler (R-Carroll), many say there is a danger that the GOP will become fragmented and rudderless.

"It was always very helpful for the minority to have a friend (in the governor's office)," says Del. Vincent F. Callahan, a Fairfax Republican who is in line for the minority leader's job. "Now we'll have to look within our own ranks. It'll be a whole new ball game."

Some of that fragmentation is sure to show up when the General Assembly begins considering the state budget, which Robb has said will reflect massive federal funding cuts and a shortfall of at least $1 billion. So far, Robb has not indicated how he plans to handle the problem, but there are only two solutions -- tax hikes and program cuts -- and either will cause a heated controversy.

So will any proposals for tightening the state's weak conflict of interest laws. Virginia's legislators last year refused to impose stricter disclosure rules on themselves or establish an ethics commission.

Many now say that Miller's defeat will spur new action -- not because most lawmakers have changed their views, but because allowing each member to determine what he believes is a conflict can, as in Miller's case, lead to unpredictable and fatal problems at election time.

"I think we should be able to get something done this year," says Sen. Adelard L. Brault (D-Fairfax), one of the Senate's leading advocates of ethics reform. "A lot of people got very upset about this Nathan Miller thing."

Supporters of the Equal Rights Amendment are also hopeful that this fall's house elections will help their cause, claiming that they picked up three pro-ERA delegates and were instrumental in Geisler's upset loss. "Overall, we're feeling good about the election," says National Organization for Women president Eleanor Smeal of Fairfax County. "It couldn't do anything but help."

Many ERA backers in the House, however, are openly skeptical of the amendment's chances for surviving in the House Privileges and Elections committee, the panel which has repeatedly stopped the measure in previous years. House Speaker A.L. Philpott (D-Henry), who opposes the amendment, previously has appointed committee members who reflect his own anti-ERA views.

Robb is expected to work more closely with legislative leaders than did outgoing Republican Gov. John N. Dalton. Robb is a Democrat with a Democratic legislature, and he also avoided taking campaign stands that might alienate them. He stuck to an uncontroversial program for economic development and steered clear of strong stands on controversial issues like taxes and the ERA.

Robb will be aided in his legislative chores by Davis, who will preside over the Senate as lieutenant governor. Davis is expected to be crucial to Robb's legislative strategy, both because he is a longtime friend of Senate Majority leader Hunter B. Andrews and because he thrives on the backroom wheeling and dealing that are the lifeblood of the assembly.

Andrews and Robb have frequently been at odds in the past. When Robb was presiding over the state senate as lieutenant governor, for instance, Andrews referred to him derisively as "Chuckie Bird". Robb's new power, some say, will do much to cool Andrews' old dislike.

"It's going to be different between them now," says Stambaugh. "Now Chuck has cards to deal back at Hunter. He didn't have any cards to deal as lieutenant governor, and now it's his deck."