Any day now a member of Congress who is wavering on the bitterly contested common site picketing bill may find a building contractor from back home on his Capitol Hill doorstep, courtesy of a nationwide "fly-in" program by industry lobbyists.

He probably has already received hundreds of little red. White and blue postcards, courtesy of the construction unions' lobby.

The member will be bombarded with reputedly scientific polls, including one form proponents showing that most people support the bill and one from opponents showing that most people oppose it, backed up by scholarly economic impact statements that contradict each other.

Common site - which would permit a union to picket and thus possibly shut down an entire construction site even if its grievance was with only one subcontractor - has become a curcial early test for a labor and its ambitious legislative program in the 95th Congress.

It has also, in the view of Labor Secretary Ray Marshall and others, become a symbolic flashpoint for union and industry that transcends its substantive importance, standing in the way of large efforts to overhaul haphazard labor-management relations in the huge, balkanized and economically ailing construction industry.

The symbolism, as much as the substance, has made the bill a multimillion-door lobbying target in Congress. Defeat could signal deep trouble for the rest of labors agenda, including repeal of Section 14(b) of the Taft-hartley Act that permits states (20 as of now) to enact "right-to-work" laws banning union shops and, more importantly, labor's drive for an overhaul of basic labor laws to make it easier to organize and negotiate contracts.

"If they can't get situs, then they're out of luck with 14(b), said Reed Larsen, executive vice president of the National Right to Work Committee. The million-member Falls Church-based group, which was instrumental in prodding President Ford into vetoing a common site bill, is mounting a massive campaign to defeat the measure this year in hopes of squelching the 14 (b) drive in advance.

While labor won't fold its tent if the picketing bill fails, "it would make it a lot more difficult . . . we'd get a lot more heat," said Robert A. Georgine, who, as president of the 4.1-million-member Building and Construction Trades Department of the AFL-CIO, is spearheading the fight for the bill.

The construction unions began their mailing blitz a month ago, providing members 1.5 million packets of flyers and postcards that are to be sent on to the White House and specifically targeted senators.

The unions are concentrating on the Senate because the key vote could come on breaking the opposition's promised filibuster, which would require 60 or 100 votes. President Carter has pledged to sign the bill if certain conditions are met, but the unions remember how a torrent of mail helped convince Ford to veto the 1975 bill after initially saying he would sign it.

While the unions are relying largely on their own membership and on political loyalties among the big Democratic majorities in both houses, industry opponents are mounting a massive public relations campaign that could cost about $1 million, according to Scott Robertson, spokesman for Associated Builders and Contractors, Inc.

The Right to Work Committee says it spent about $700,000 in 1975 and could spend that much again if the fight lasts longer than a few months.

Labor estimates its costs at about $150,000, but that doesn't count its regular propaganda apparatus, including newsletters and other intramural channels.

According to Robertson, the industry's lobbying arsenal includes three public relations agencies, a U.S. Chamber of Commerce-produced slid show that is currently being shown "to anyone who'll watch" across the country, plans for dispensing up to 500,000 letters and postcards for mailing to Congress and the White House, and a stable of about 100 lobbyists for direct contact with members of congress. The Builders and Contractors group has flown in about five builders to bring hometown pressure on their congressmen so far, said Robertson, and plans to airlift in many more.

The Right to Work committee has sent out 700,000 letters to member so far, all with the customary fund-raising pitch, and plans full-page ads in newspapers in eight states, concentrating on senators deemed vulnerable to such pressure. 'We're trying to make the issue too hot to handle." said committee spokesman Herb Berkowitz.

Largely overlooked in the thunder of rhetoric form both sides is a provision in the bill to help standardize collective bargaining in the construction industry, which has been marked by widely varying settlements and "leapfrogging" of wage increases among the 10,000 locals in the 18 building trades unions.

Although the economic slowdown has moderated increases in recent years, contract settlements in boom year 1970 produced average raises of nearly 15 per cent, twice the rate of increase for manufacturing, and some economists fear a resumption of inflationary settlements when conditions permit.

Labor Secretary Marshall has endorsed the picketing proposal but said he considers the standardized bargining provisions more significant. President Carter signalled, through Marshall, that he wants the bargaining section and might not sign the bill without it.