The only time that partisan control of the Senate changed in mid-session, historians say, was in 2001. Republicans began the year controlling the 50-50 chamber with Cheney's tie-breaking vote. But Democrats, mindful of the recent sudden death of Sen. Paul Coverdell (R-Ga.), were aware they could be a heartbeat away from the majority.
In order to adopt new rules organizing the Senate, the two parties must reach nearly unanimous agreement. Democrats in 2001 blocked the naming of committee chairmen and members, demanding concessions before agreeing to the rules. Among those concessions: Should the numerical advantage change, all committee assignments and chairmanships would be nullified, and a new organization would have to be submitted.
That's what happened, not because of a death but because disgruntled moderate Republican Sen. James M. Jeffords (Vt.) decided to caucus with the Democrats, giving them a 51-49 edge and the powers of the majority. Senate Republican sources said yesterday that their party is likely to press for similar concessions when negotiating the operating rules for the next Congress. But even if Johnson were incapacitated, Democratic aides say, they would resist.
A different scenario unfolded in 1954, after the deaths and replacements of several senators over two years. Republicans remained the majority party even though Democrats eventually outnumbered them, 48 to 47, with one independent. Democratic leader Lyndon B. Johnson did not challenge the GOP's control, in part, historians said, because the independent, Wayne L. Morse of Oregon, warned that he would caucus with the Republicans if need be. That would have led to a 48-48 chamber, and Vice President Richard M. Nixon would have broken the tie in Republicans' favor.
http://www.washingtonpost.com/wp-dyn/content/article/2006/12/14/AR2006121400379_2.html