Republican Sen. John W. Warner already has raised nearly $600,000 for his 1984 reelection campaign and expects to pass the $1 million mark by the end of the year, while Virginia Democratic party leaders remain unable to find a candidate to oppose him.

The Warner war chest -- compiled in a series of fund-raising dinners and private parties during the past seven months -- has alarmed some Democrats who fear the freshman GOP senator may be on his way to building an insurmountable lead in fund-raising.

Several Democratic leaders said yesterday that if a credible candidate does not surface soon, the party may forfeit any chance of mounting a serious challenge to Warner, resulting in its second successive Senate defeat in two years.

"They may have to look at the damn choice of letting him go unopposed," said Sen. Richard L. Saslaw (D-Fairfax). "I'm sure we'll put up some nominee. The question is, how serious?"

The Democrats' frustration is compounded by a widespread belief that, with the right candidate, Warner could be vulnerable.

Elected by a razor-thin 4,720 vote margin in 1978, the 56-year-old Warner no longer has the aura that he gained by campaigning with his wife, actress Elizabeth Taylor. The Warners were divorced last year.

Yet, says Democratic state Del. Alson H. Smith, a key party fundraiser, "If there's any candidate on the horizon right now, I haven't heard about it."

Democratic Gov. Charles S. Robb is viewed by many party leaders as the one candidate with sufficient voter appeal to beat Warner. But when a group of state senators met with him three weeks ago and implored him to consider the race, Robb repeated what he has frequently said publicly: that he has no intention of running for any office until his term is up in January 1986.

That leaves the party with a stable of reluctant officeholders, many of whom, as conservatives, would probably find it difficult to position themselves against Warner, some party officials say. State Attorney General Gerald L. Baliles, House Appropriations Committee chairman Richard Bagley of Hampton and, to lesser degree, Senate Majority Leader Hunter B. Andrews, also of Hampton, have set on their sights on running to succeed Robb in 1985.

Lobbyist and Robb political confidant William G. Thomas from Alexandria, who was toying with running for the Senate as recently as this spring, has yet to signal that his interest is serious.

The only person to announce is former state delegate Edythe Harrison, a party maverick from Norfolk who was defeated in a bid for reelection last year.

As a result, some party leaders fear, they are facing a situation identical to last year when Democrats agonized over a candidate right up to their June nominating convention, allowing GOP candidate Paul S. Trible to raise enough money to put together his ultimately successful statewide organization.

Warner already has begun doing that, using his incumbency to maximum advantage.

According to a mid-year report released yesterday, the senator raised $442,625 by June 30, including $171,557 from corporate and ideological political action committees.

The senator, who sits on the Armed Services Committee and the Energy and Natural Resources Committee, received $45,800 from defense contractors and more than $18,000 in PAC money from oil conglomerates, coal companies and electric utilities.

In addition, Warner spokesman Andy Wahlquist said, another $150,000 came in during July and Warner expects to surpass $1 million by the end of December.

As for the Democrats' problems, Wahlquist had his own interpretation: "If you've got a good senator who's doing what you like, why run anybody against him? Maybe he's just doing a good job."