The deadline to file the 4,500 signatures of registered voters needed for the May primary was noon Tuesday. Since no Democrat is on the primary ballot, the Democratic state central committee has until June 30 to make an appointment.
Other names being floated are U.S. Reps. Baron Hill and Brad Ellsworth.
There is only one Democrat that was interested in challenging Bayh. However, she did not meet the deadline. So, the state Democratic Party will choose the party's nominee for the November election.
It is an election Republicans say they can win. Former Republican Senator Dan Coats and at least four other Republicans are expected to be on the ballot.
Republican Indiana State Senator Marlin Stuzman met the noon deadline to file the petition carrying the required 500 signatures to enter the Hoosier State's May primary.
Stuzman and others in his party believe they have a real shot at the Senate seat now that Bayh has decided to call it quits.
"I think our chances in the fall are really good right now, so we are excited about the position we are in," said Stuzman, (R) U.S. Senate candidate.
But, Indiana Democrats say, do not count them out.
"It's an imminently winnable seat for the Democratic Party, and do think you'll see a number of names now floated," said U.S. Rep. Peter Visclosky, (D) Merrillville.
Political experts question Bayh's timing.
"I don't quite understand why a person who is that fed up with Washington would show his frustration the day before people could file for his office in his own party," said Paul Green, Roosevelt University.
Bayh said his frustration with extreme partisan politics is one of the reasons he decided not to run for re-election.
"There is just too much brain-dead partisanship, tactical maneuvering for short-term political advantage rather than focusing on the greater good," said Bayh.
"There are a lot of people -- particularly in the House of Representatives who I'm familiar with -- on both parties who get along well, who solve problems and are there to make the world a better place," said Visclosky.
Congressman Visclosky said he believes partisan politics is more of a perception than a reality because extremes from both parties are the ones that dominate the news.
Visclosky said he is not interested in Bayh's seat.
The Associated Press contributed to this report.