The vote, which was in favor of Mr. LaMarre, was one short of the two-vote majority needed to win.
Republicans had only a two-vote majority in the 108th Congress, so they were in a weak position to implement this procedural maneuver.
But the picture is quite different in the Senate, where Republicans have a two-vote majority and do not have the 60 votes they need to end a filibuster.
Republicans hold a two-vote majority in the Senate, and some leading Republicans, including President Bush, had urged Mr. Nickles to stay.
This year, each of the Senate's 17 legislative committees has a two-vote Republican majority.
With Republicans holding only a two-vote majority on the panel, a defection by Mr. Chafee would have deadlocked the committee.
The vote went to Bloemfontein with a two-vote majority.
A year earlier, the midterm congressional elections had ended six years of Democratic control in the Senate, giving the Republicans a two-vote majority.
He eked out a two-vote majority in that vote, which authorized him to send German troops to participate in a combat role outside Europe for the first time since 1945.
The prime minister's coalition held a two-vote majority, but he says the president's actions have increased his strength.