The House rejected an amendment in March that would give union members the right to keep their dues from being spent on political activity.
Lawmakers are likely to reject the proposal again when the issue resurfaces on the floor.
The AFL-CIO and most Democrats oppose the measure. Republicans generally favor it, since organized labor generally backs Democratic candidates. The GOP sources, who spoke on condition of anonymity, said Wilson is concerned that a negative vote on the House floor could cause a statewide ballot issue on the same subject to lose momentum. At the same time, House Republicans believe that passage of the California initiative would give impetus to the issue when it comes up on the House floor. Confronted with a rebellion within his own ranks, Speaker Newt Gingrich agreed recently to allow an open debate on campaign finance legislation before Congress' Memorial Day recess.