WASHINGTON (CNN) -- With Democrat's grasp of the Senate relying on the thinnest of margins, ultimate control of the chamber hung on the health of a South Dakota senator who underwent brain surgery Thursday morning. Sen. Tim Johnson of South Dakota was in critical condition, said David Boyd, a nursing supervisor at a George Washington University Hospital. Should Johnson not be able to complete his term, which ends in 2008, South Dakota Gov. Mike Rounds, a Republican, would appoint his replacement, which could shift the balance of power in the Senate.