The speculation comes less than two weeks after Bayh hired campaign staff and announced plans to form a fundraising committee for a potential presidential bid.
"He has this very serious team ... some very high-powered help," Mark Blumenthal — aka Mysterypollster, editor of pollster.com — said at the time. Blumenthal noted that he's worked in the past with some of Bayh's new staff.
Bayh might have been a strong Democratic contender in a presidential race. A two-term governor before being sent to Washington, Bayh would have come to the contest with the advantage of having both Capitol Hill and gubernatorial experience.
"He also has the credentials of being both a popular senator and former governor in a red state, and he's a Midwesterner, which may translate into appeal in Iowa," Blumenthal said of Bayh recently.
Just last Sunday, Bayh spoke in New Hampshire, the state with the first presidential primary, on energy independence, global warming and the war in Iraq.
The Indiana senator has situated himself as a centrist, stressing, according to his Web site, "fiscal responsibility, lower taxes, job creation and lean government."
Bayh also promotes himself as a moderate who can work with Republicans. Bayh chaired the centrist Democratic Leadership Council for four years and is active in bipartisan efforts in Congress.
But Bayh still lacks name recognition, and most recent polls have had him between 1 and 3 percent.
This has been a busy week in the 2008 race. Monday, Republican Sen. Sam Brownback said Monday he is taking the first step toward launching a bid for the 2008 Republican presidential nomination.
A vigorous abortion opponent, the Kansas senator pledged to make "issues of life," fiscal restraint and tax reform key components of his effort to woo supporters.
On Tuesday, Democratic Rep. Dennis Kucinich of Ohio launched his second bid for president, a long-shot candidacy fueled by his frustration with his party's effort to end the Iraq war.
"I am not going to stand by and watch thousands more of our brave, young men and women killed in Iraq," Kucinich said in his announcement speech. "We Democrats were put back in power to bring some sanity back to our nation."
So far most of the attention has focused on possible frontrunners such as former Democratic Sen. John Edwards, Sens. Barack Obama and Hillary Clinton, former Vice President Al Gore and, on the Republican side, Sen. John McCain, Govs. Mitt Romney and George Pataki, and "America's Mayor," Rudolph Giuliani.
Former NATO Commander Gen. Wesley Clark, Former Health and Human Services Secretary Tommy Thompson, former House Speaker Newt Gingrich, Govs. Tom Vilsack, Bill Richardson,and Mike Huckabee, Sen. Joe Biden, and Rep. Duncan Hunter are also all either running or considering runs.