President Carter will sign a controversial bill to expand unions' picketing rights at construction sites that was vetoed last year by President Ford, Labor Secretary Ray Marshall told a House subcommittee yesterday.

Marshall said Carter will sign the bill so long as it includes an exemption for residential construction and provisions aimed at coordinating the fragmented collective bargaining procedures in the building industry.

The main provision of the bill, which was reintroduced after Ford's veto, would permit a union with a grievance against one subcontractor to picket an entire construction site, possibly shutting down the overall project.

The veto caused the resignation of then-Labor Secretary John T. Dunlop and set the stage for this year's fight, which is viewed as the opening battle in a major effort by labor to win widespread gains, including repeal of the legislation that permits state right-to-work laws. Carter said during the campaign he would sign both the picketing bill and the right-to-work repealer but would not lobby for their passage - a position he apparently intends to maintain.

"Unfortunately, common situs (the picketing legislation) appears to have taken on a symbolic significance which far exceeds the actual impact which it is likely to have on the construction industry," Marshall said in testimony before the House Labor-Management Subcommittee.

But so long as the picketing issue is unresolved, it will be "considerably more difficult for labor and management to address the unique problems which beset the construction industry," including widely varying contract settlements and labor market instability, Marshall said.

He said the bargaining provisions of the bill would mitigate these problems by creating a Construction Industry Collective Bargaining Committee and a mechanism for approval of local bargaining settlements by their national parent unions.

In defending the picketing provisions, Marshall said they would give construction workers the same rights that industrial workers already have.

He disputed allegations by the construction industry, which has mounted a major lobbying campaign to defeat the measure, that the bill would lead to total unionization of the construction industry.

"The legislation may have the effect of encouraging more job sites which are exclusively union or exclusively nonunion," he said, adding that this may be more conducive to industrial harmony, productivity and effective management.