The Senate, angered by a Communist couple from rural Virginia enrolled in a federal job skills program, has voted unanimously to deny federal training or employment to anyone who publicly advocates the violent overthrow of the government.

The Senate voice vote, which some say raises constitutional questions about freedom of speech, was directed at Dorothy and Allen Blitz of Martinsville in southern Virginia. The Blitzes, a couple in their early 30s who say they support the armed overthrow of the government are learning how to become a brick mason and a carpenter under a federal job training program.

Rep. W. C. (Dan) Daniel (D-Va.), whose district includes the mill town and is infuriated by what his constituents call "the Blitz situation," persuaded Sens. Ernest F. Hollings (D-S.C.) and Harry F. Byrd (Ind-Va.) to introduce the training and employment ban.

"I just don't want anyone who advocates the overthrow of the system benefiting from that system," said Daniel, a six-term conservative who last month introduced a similar bill in the House. The House is expected to consider the Senate measure today as an amendment to the federal government's omnibu spending bill for fiscal 1981.

On the Senate floor Thursday, Sen. William Proxmire (D-Wis.) joined the Southern conservatives and spoke in favor of the measure. It would prohibit the Blitzes from continuing to earn $3.10 an hour while working 35 hours a week in the Virginia program, funded by the Comprehensive Employment Training Act (CETA). "I don't know how anybody would possibly object to this amendment," Proxmire said.

Objections, however, were voiced yesterday by prominent civil rights attorney Joseph L. Rauh of Washington, who accused Congress of "learning little from the old McCarthy days." Rauh, a veteran liberal lawyer and leader of Americans for Democratic Action, said it "hardly seems sensible" that the ban is moving through Congress at the same time that it is considering abolishing the Smith Act. That 1940 law, which has not been enforced for the last 20 years, makes it a crime to advocate the forcible or violent overthrow of the government.

"The defeat of McCarthyism in the '50s inoculated this country against this sort of thing," Rauh said. "What frightens me is that the inoculation appears to be wearing off."

Byrd, a Virginia newspaper publisher, said yesterday that the Senate vote has nothing to do with freedom of speech. "I think the Blitzes should have freedom of speech. But should the taxpayers funds be used to subsidize this?" asked Byrd."This is not a question of freedom of speech, anyhow. They are being deprived of no civil rights that I can see. Congress has the right to circumscribe the way tax funds are expended."

According to Wesley McCune, who monitors rightest political groups for Group Research, a Washington-based organization, the Senate action represents a change of course for Congress. "I can't remember congressional reaction of this sort since the House Un-American Activities Committee was folded in January 1975) after the Watergate reforms," said McCune.

In addition to pressure from Congress, the Blitzes have been severely criticized in their hometown, a furniture and textile producing community of 20,000 near the North Carolina border. They are double cursed in conservative Martinsville, where communism is a synonym for evil and where government handouts are viewed as a form of perverse socialism.

"I think the vast majority of people around here would be pleased to see the communists move on out of here," said City Councilman Francis West, echoing the sentiments of many in a region that's considered the conservative core of a conservative state.

No one, however, has been more furious than area congressman Daniel, a former national commander of the American Legion who was born on a poor dirt farm and made himself a success the bootstrap, all-American way.

Daniel, a 66-year-old politician who's never seriously been challenged since he won his seat in 1968, defended his proposal as a service to his constituents. "The majority of the people in my district would be referred to as God-fearing people, and communism is atheistic." His voters "would have a minimum of high regard for anyone who calls himself a Communist," he says.

"But we have to eat," argued Allen Blitz, 33, the son of a Bronx carpetlayer who calls Daniel a "bourgeoisie oppressor." Blitz said that he, his wife and their 3-year-old daughter Kendra are poor and fully qualify for the federal aid they receive.

Under existing CETA law, local officials say the Blitzs cannot be denied enrollment in the program without endangering its funding.

The Blitzes have refused to suffer silently the anger of Daniel and his supporters in Martinsville. "We've fed the hand that feeds us for years," protested Dorothy Blitz, 34, a former elementary school teacher turned waitress turned labor organizer and revolutionary. "We paid our taxes like anybody else and we are entitled to this program."

They both were working -- and paying taxes -- until Nov. 3, 1979, when they went to Greensboro, N.C., to take part in the demonstration that left five other Communists dead after a gun battle with members of the Ku Klux Klan. The Blitzes, who earlier, became radicalized while living in North Carolina, saw three close friends die within a few feet of them during the Greensboro "Death to the Klan" protest that was sponsored by the Communist Workers Party.

The Blitzes were indicted on state felony riot charges, that were dropped last month. But they both lost their jobs in the resulting controversy over the incident.

Out of work and running low on savings, the Blitzes last summer turned to the CETA program, which is administered by nearby Patrick Henry Community College and is considered a model program in Virginia. "After we got fired, you know, it was real hard to find a job in a small southern town like this," said Dori Blitz.

The Blitzes say they work hard for their CETA money (they recently were working laying 7 1/2-inch concrete blocks at the city ballpark), and they accuse Daniel and others of harrassing them and violating their constitutional right to free speech.

"I believe that communism also stifles free speech," Daniel responded. "I don't believe the people in Poland will have very much liberty if there is an invasion by the Communists."

Daniel quickly dismissed the Supreme Court rulings permitting individuals to advocate violence in public as long as they don't precipitate actual violence. After the ruling in Yates v. U.S. in 1957, prosecutions under the Smith Act dwindled and died out. Said Daniel: "There are a lot of Supreme Court decisions that I don't agree with."

Councilman West called the entire CETA program, which has been plagued with scandals, a "boondoggle." After complaining about the Blitzes to the Virginia community college board, of which he is a member, West persuaded the state to investigate all CETA programs affiliated with the community college system.

The Blitzes, who will end their CETA training in early spring, said the local furor has renewed their commitment to stay in Martinsville and prepare for the workers' revolution they claim that their persecutors are hastening.

"We will never not be Communists," said Allen Blitz. "That's what freaks out the bourgeoisie."