Brandishing a General Accounting Office report that supports their cause, congressional conservatives kicked off a drive yesterday to scuttle the nearly half-century-old Bacon Act - one of organized labor's holy writs.

The legislation requires that workers on federally subsidized construction projects be paid the local "previling" wage, which contractors complain usually means union-rate pay.

While unions describe the law as a matter of equity, critics, including the GAO, charge that it adds hundreds of millions of dollars a year to construction costs, and thereby fuels inflation.

The fight over Davis-Bacon, which has prompted a flurry of propaganda and lobbying from both sides, is expected to be the major labor-business confrontation in this session of Congress.

The fact that the major showdown is occuring over legislation that has been on the books for 48 years underscores the labor movement's waning influence in Congress, which last year shelved a comprehensive revision of labor laws and shot down several other union-backed bills.

But the push for Davis-Bacon repeal is not expected to be easy. Subcommittees and committees with jurisdiction over labor legislation are considered unlikely to approved a repeal bill, and the Carter administration has pledged to veto any repeal legislation.

Consequently, the Davis-Bacon critics - led by Sens. John G. Tower (R-Tex.) and Orrin G. Hatch (R-Utah) and Reps. Tom Hagedorn (R-Minn.), John Erlenborn (R-Ill.) and John M. Ashbrook (R-Ohio) - are planning what Tower called a "rifle-shot" attack as well as a general assault.

The idea is to repeal Davis-Bacon provisions, program by program, as each authorization or appropriations bill comes along, starting this week with hearings on military and housing construction bills. This approach avoids hostile committees and puts President Carter in the sometimes vulnerable position of vetoing major legislation just to strike down an objectionable rider.

The critics also are pushing for hearings on the overall repeal legislation, which has been introduced in both houses. No hearing has been scheduled on the comprehensive bill.

Tower said yesterday he sees a "serious chance" for the rifle-shot approach but is "less than sanguine" about across-the-board repeal.

Davis-Bacon's critics are relying heavily on the recently released report from GAO, the congressional watchdog agency, that calls the act unnecessary, outdated, wasteful, unfair and inflationary. The study dismisses White House efforts to tighten up on Davis-Bacon enforcement by administrative action and it calls for repeal.

Labor Secretary Ray Marshall, who was accused in the report of making a misleading defense of Davis-Bacon in comments to the GAO, responded that, as a former economics professor, he would have flunked the people who compiled the report if they had done it for one of his classes.

In their news conference yesterday, the Davis-Bacon critics indicated they will attempt to turn the fight into a major political issue.

Calling Davis-Bacon an "economic dinosaur," Tower said Vice President Mondale's recent assertion that Carter would veto any repeal legislation "make(s) a mockery of the president's promise to fight inflation and eliminate government regulations which feed that inflation." Erlenborn called the legislation a "federal giveaway" that gives "unfair advantage to that small minority of Americans who are in the construction unions."

The GAO report concluded that Davis-Bacon adds "several million dollars annually" to the cost of public works projects. Hatch said the figure is more like $2.7 billion a year.