Lobbyists for Common Cause and the AFL-CIO, who often find themselves working together, will be cold-shouldering each other today and Tuesday, at least on the House side of the Capitol building.

The two groups are working very different sides of the street on a pending bill (due for House debate and a vote Tuesday) that would grant full partisan political participation rights - as candidates, managers or money-raisers - to the nation's 2.8 million federal and postal employees.

Federal civil servants are now limited to passive roles in partisan elections. They can vote, give money and act as low-level campaign workers in partisan elections now, but they cannot run campaigns, or campaign for candidates because of the Hatch Act. That is a 38-year-old collection of administrative rulings originally designed to insulate the federal bureaucracy from politicians.

On Tuesday the House will take up - and, insiders believe, pass - a bill by Rep. William Clay (D-Mo.) to reform the Hatch Act. In effect it will remove most of the "no-no's" on political activity (off the job) but retain, backers say, all of the protections against arm-twisting of federal employees to work for the party in power.

Common Cause generally considered a "liberal" citizens lobby, stunned some House members and infuriated the AFLO-CIO by coming out against any changes in the Hatch Act.In effect, it said that the political freedoms that would be granted government workers are outweighed by the potential for mischief if government workers plopped into the political mainstream.

Since Common Cause came out against Hatch Act changes, an active group of Washington area members - most of them federal employees - have tried to get the parent body to change its stand.

Some Common Cause members argue that the poll their organization took to back its stance wasn't big enough, or representative enough to merit opposition to Hatch Act changes. They also say they had no input in the decision. Although it has fewer than 280,000 dues-paying members (as opposed to the millions in the AFL-CIO) Common Cause has a lot of clout in Congress, especially with liberals, and the emerging "suburban" majority representing both the Democratic and Republican sides of the Senate and House.

AFL-CIO lobbists have pulled out all stops in their drive to get the Hatch Act amended. Most government union members are affiliated with the AFL-CIO and the unions see a totally enfranchised bureaucracy as a way to increase their clout with Congress.

Government workers represent the largest, best paid and most strategically located group of voters in the country and they have been relatively untapped as a source of talent, muscle and money, in politics.

Local Common Cause dissidents hoped to turn their national governing board around in its Hatch Act opposition. They met at headquarters last Tuesday evening, accompanied by some supporters from the unions, to state their case for reconsideration.

Common Cause brass say that the organization's Hatch Act stand will be presented to the issues committee when it meets - in July. That doesn't mean the policy will be changed, and it certainly means there will be no change before the important House vote set for June 7.

Common Cause officials say they will be lobbying against Hatch Act changes this week. ALF-CIO officias say they will be lobbying for the Hatch Act changes. Both sides will be counting heads when the House votes, and that squeeze could result in some key members' suddenly developing colds, or being recalled home for urgent business on the theory that there are two important sets of toes that are too important to step on right now.