The National Association of Manufacturers, following in the footsteps of other major business groups, yesterday reached broad agreement on the role of the federal government in providing child care.

The association acknowledged that the growing need for child care must be addressed nationally, but said that a "bottom-up" approach should be taken, leaving as much control as possible at the local level.

"We are looking for a program which provides to the community and employers a degree of flexibility in designing solutions to child care best suited to that locale," said Pete Lunnie, the association's director of employee relations.

The association's subcommittee on employment and training, made up of representatives of 25 member companies, also said "the very real problem of liability for providers and users" must be addressed and any national child care program "has to be guided by the fiscal realities of the budget."

The association's action came on the heels of last week's decision by the Chamber of Commerce to endorse the concept of federal child care legislation. There are two major legislative proposals moving on a fast track in Congress to accomplish that objective, perhaps by the end of the year.

The issue of child care, driven by changing work place demographics and the fear of labor shortages, has in the last few months been pushed high on the nation's legislative agenda. Supporters of a national child care policy also have been pushing presidential candidates to make commitments on the issue.

Like the Chamber, the National Association of Manufacturers has not endorsed any specific piece of legislation, but the bill that most closely satisfies its objectives is the one that has been introduced by Sen. Orrin Hatch (R-Utah), said Lunnie.

The Hatch bill offers incentives to business for setting up child care centers, addresses the issue of liability and leaves regulation to the states.

The competing legislation has been offered by Sen. Christopher Dodd (D-Conn.) and would use a program of federal block grants to provide child care for low- and moderate-income families.

The first congressional hearings on the Dodd proposal will begin Feb. 25.

The association, which formulated a policy on corporate programs for working parents in June 1986, said one purpose in coming up with a specific position on child care is to have a voice in the legislative debate on the issue.