Nebraska Governor Dave Heineman said Monday afternoon it could take several weeks to find someone.
On Saturday Rick Sheehy suddenly resigned after state records showed he had made thousands of calls to four women on his state-issued cell phone.
Heineman says the state constitution prohibits any current state senator from being appointed while the legislature is in session. He says he wants to make a decision as soon as possible.
Heineman says he is looking for someone who won't run for governor in 2014. He says he doesn't want to give an advantage to any possible candidate in the Republican primary race.
Heineman says Sheehy resigned after he became aware of "new and more information.'' But Heineman acknowledged Monday that he had confronted Sheehy about past rumors.