In a vivid display of President Obama's diminished clout, the Senate's newest Republican and two veteran Democrats Tuesday helped block Mr. Obama's bid to fill a key labor post with a nominee they considered too cozy with unions.

With newly seated Sen. Scott Brown, Massachusetts Republican, voting to sustain the filibuster, Senate Democratic leaders failed to muster the 60 votes needed to force a vote on the nomination of Craig Becker to the National Labor Relations Board, which resolves disputes between unions and management.

Dubbed a friend of organized labor, Mr. Becker had been fiercely opposed by business and employer groups, who feared his support for the proposed Employee Free Choice Act, called "card check," which would give unions a stronger hand in organizing employees. Republicans strongly oppose the legislation, which could come up for a vote in the Senate later this year...