Fairfax County prosecutor Robert F. Horan, known for his tough stand on law-and-order issues, yesterday made a strong pitch to old-fashioned liberal economic themes as he launched his campaign to become Virginia's Democratic nominee for the U.S. Senate.

Horan, 49, this week became the first candidate to break a weeks-old deadlock among Virginia Democrats and declare himself a candidate in the chaotic scramble for the party's nomination, to be decided at a convention in Roanoke on June 4 and 5.

At a press conference attended by a handful of supporters, Horan denounced the Reagan administration yesterday for "cold hearted and callous" policies and invoked the philosophies of Franklin D. Roosevelt's New Deal.

"I believe the function of government is look out for those who cannot look out for themselves," said Horan, saying "trickle down" economic politices have failed. "Who is better able to tighten their belts in these difficult economic times, the crowd who makes over $200,000 or the unemployed? It seems to me Congress has to face up to that priority."

Horan, regarded as an effective and forceful campaigner, also took after Newport News congressman Paul S. Trible, the apparent Republican nominee to succeed retiring Sen. Harry F. Byrd Jr., saying Trible has "wrapped himself around the trickle down theory."

Trible "has been sitting there for four months just collecting money without ever being forced out in the open on issues like unemployment," Horan said.

With only eight days to go before the nominating convention, Horan admitted he will have to make personal appeals to the 3,624 convention delegates, of whom almost 700 are from Northern Virginia.

So far, Horan's major declared opponent is considered to be State Sen. Virgil Goode, 35, of Rocky Mount, a self-styled populist. Others who have declared are Del. Floyd Bagley of Prince William County and Peter Tsakanikas, a businessman from Rosslyn.

His most formidable opposition may come from former Congressman Joseph L. Fisher, now a member of Gov. Charles S. Robb's cabinet, whose candidacy would seriously cut into Horan's support among the Northern Virginia delegation. Fisher is expected to announce his intentions later this week, as will Del. Norman Sisisky of Petersburg, a wealthy beer and soft drink distributor promoted by the state's conservative business establishment.

Spurred by what he perceived as the party's fixation with candidates' ability to raise money, Horan said yesterday he thought he could run for the Senate on $1 million. He described the response from fundraisers as "fairly encouraging" so far, but insisted his would be strictly a "pay-as-you-go" campaign.

No ranking Democrats were present at Horan's announcement in the basement of the Fairfax County Administration building, although the candidate said he expects support from State Sens. Richard Saslaw of Fairfax, Charles Colgan of Prince William and a network of county prosecutors from around the state.