Virginia Democrat Andrew P. Miller said yesterday he does not expect actress Elizabeth Taylor to become an issue in his campaign for the U.S. Senate.

Miller, who is opposing Taylor's sixth husband, former Navy secretary John Warner, in the Senate said, "I don't think Mr. Warner intends to campaign against my wife and I don't intend to campaign against his . . .

"What Liza may do for John is her affair."

Miller made the comments in response to questions at a news conference as a day of partisan potshots livened Virginia's newly restarted political campaign.

Earlier in the day, at a news conference in the Capitol, Virginia Gov. John N. Dalton said he was "surprised" at Miller's recent allegations that Warner has been something less than a true Virginia resident. Warner, at least, "stayed in Virginia to go to college" at Washington and Lee University, Dalton said, while "Mr. Miller went to a school in New Jersey" (Princeton).

Meanwhile in Norfolk, former chief of naval operations Elmo R. Zumwalt - who worked under Warner in the Navy - described his former boss as a "dilettante . . . who doesn't do his homework" and would be "a very inferior senator."

Interviewed by a Norfolk newspaper Zumwalt said Miller would be a better senator than Warner but that Republican Richard D. Obenshain - who died in an Aug. 3 plane crash - would have been better than both of them.

Zumwalt , who ran unsuccessfully as a Democrat for Virginia's other U.S. Senate seat two years ago, said Warner inherited Obenshain's GOP nomination because of "Elizabeth Taylor's fame and Cathy Mellon's money."

About half of Warner's estimated $7.5

Zumwalt said his belief that Obenshain would have made a better senator than Miller is based more on personality than philosophy.

Zumwalt said he attained a high degree of respect for Obenshain during his unsuccessful attempt to unseat independent Sen. Harry F. Byrd Jr. in 1976. Obenshain's efforts as cochairman of Byrd's campaign, Zumwalt said, were "effective, organizationally sound and very clean."

"He was a man of total integrity, although I didn't agree with him on many issues," Zumwalt said.

Asked if he also considered Miller a man of "total integrity" Zumwalt replied: "much more than John Warner."

Warner's campaign office said the candidate would have no comment on Zumwalt's remarks.

Miller, advised of Zumwalt's comments, said he was "delighted he thinks I am the superior candidate with respect to the race we actually have at hand."

At his news conference Miller also issued a financial statement that he said was intended to update a similar financial disclosure he made last year while running for governor.

It showed assets of $325,905 - including $185,187 in securities - and liabilities of $44,652 consisting of two real estate deeds of trust.

If elected, he said, he probably would put the securities in a blind trust.

Miller also said he would hold four debates with Warner on campaign issues. Debates between Miller and Obenshain had been scheduled before Obenshain's death.

Dalton, at his news conference in the Capitol, also reported final figures showing the state with a budget surplus of $39.7 million for the 1976-78 biennium.

Dalton said the final figures were largely the result of a 5 percent reduction in state expenditure ordered across the board by former governor Mills Godwin last year when the state appeared threatened with a budget deficit due to inflation and the sluggish economy.

Had Godwin not ordered the cut, Dalton said, the state would have ended the period with a $20 million deficit.

The governor said the $39.7 million - which he preferred to call an "unappropriated balance" - will be added to the general fund revenues for the 1978-80 biennium.