The AFL-CIO dominated drive to unleash nearly 3 million federal secretaries, scientists and letter carriers for more active roles in partisan politics may have hit a real snag.Reason: the close, stunning defeat big labor suffered Wednesday when the House shot down a "must" bill dealing with construction industry strike rights.

Although the common site picketing bill isn't related to the move to repeal Hatch Act political restrictions on government workers, the surprisingly rought handling it got from the House may be significant when a Hatch Act reform vote somes up later.

The parallels are tantalizing. In 1976, the House easily passed the common site picketing bill - permitting a union in dispute with one subcontrator to shut down an entire construction site. It did so even though there were fewer Democrats in Congress and none in the White House.

The same thing happened with the Hatch Act reform package. The House approved it by a 288-to-119 vote and President Ford - as he did with the common site picketing bill - vetoed it. The House failed to override either veto.

This year labor thought it had a good chance to win on both bills. But construction industry brass lobbied hard and President Carter gave the bill only lukewarm support. The White House made no telephone calls to key "swing-vote" members and the common site picketing bill didn't get the swing votes it needed.

"Don't make too much of the analogy between common situs and the Hatch Act situations," a House Democratic staffer said. "But I think it is safe to say that the Hatch Act reform looked better on Monday than it did Thursday morning" after the defeat of the common site bill.

"I'd say that the Hatch Act reform plan is in real trouble only if pressure groups opposed to it muster a lot of grass-roots opposition," he speculated. "I guess what I'm saying is that labor doesn't automatically have the clout it believes it does when members start getting a lot of heat from the public in the opposite direction."

An AFL-CIO union lobbyist said he expected "both sides" to push harder on the Hatch Act issue this year. "In 1975 and 1976 we know the President would veto it. The deal was to get it through Congress with veto-oroof dent will sign pretty much whatever he gets relating to the atch Act. The problem now is to get it through Congress, period," he said.

Last year a solid bloc of AFL-CIO unions endorsed Hatch Act Act reforms that would give government employees the right to take an aative role in or manage campaigns or run as Republicans or Democrats.

In 1975 and 1976, most newspapers that commented editorially on Hatch Act changes reacted negatively. The majority tended to oppose major liberalizations, on ground that it could open up the career civil service and its 2.7 million well-paid, strategically located workers to increased political manipulation.

Backers of the bill to reform the Act say there are sufficient guarantees to prevent any arm-twisting of employees by outside politicians or supervisors hoping to curry favor with the administration in power, or local political bosses. (The Washington Post yesterday editorially endorsed changes in the Hatch Act, saying that the Act was a "good example of a well-intentioned law that has become stifling . . .")

It is easy enough to find out how most politicians feel about liberalizing the Hatch Act. The position of labor union leaders is also clearcut. The reaction of the U.S. Chamber of Commerce is equally predictable. Newspapers also have their say. Everybody, it seems, claims to speak for somebody.

Too bad somebody can't ask government workers - the people who would be most immediately and directly affected - what they think.