But Kaine, the Democratic National Committee chairman who has previously disavowed interest in the Senate seat, has been silent since Webb's Wednesday bombshell. That leaves a gathering field of potential candidates on the sideline awaiting word from Kaine.
"He's at the top of the list and I would very strongly encourage him to run," said Brian J. Moran, head of the Democratic Party of Virginia.
Added state Sen. Donald McEachin, "We only have one statewide winner. Governor Kaine is proven statewide, and, like Senator Webb, he brings the right intellectual prowess to the job."
One nationally known Democrat quickly mentioned as a contender should Kaine refuse is former DNC chairman and Clinton White House insider Terry McAuliffe.
McAuliffe, who unsuccessfully sought the Democratic gubernatorial nomination in 2009, isn't ruling out a bid for Webb's seat, said aide Levar M. Stoney. McAuliffe is better suited to being governor than a legislator, Stoney said, but for now he's focused on his clean-fuel, high-efficiency automobile venture, and not elective office.
Other prospects include Democratic U.S. Reps. Gerry Connolly and Bobby Scott, and former U.S. Reps. Tom Perriello and Rick Boucher, who were defeated last fall.
Connolly and Scott declined comment. Perriello was outside the United States and unavailable.
But privately, their aides and senior Virginia Democrats acknowledged Kaine has first refusal.
On the Republican side, George Allen, a former U.S. senator and governor, and tea party activist Jamie Radtke are seeking the GOP nomination, and others are sure to enter.
Allen, once considered a top Republican 2008 presidential prospect, self-destructed in his 2006 re-election bid against Webb after he referred to a Webb aide of Indian descent as "macaca," an ethnic slur in some cultures. Webb won by about 9,000 votes.
Kaine, the son-in-law of former Republican Gov. Linwood Holton, comfortably won the 2005 gubernatorial race after four years as lieutenant governor to popular Democratic Gov. Mark R. Warner, now Virginia's junior U.S. Senator.
He presided over Democratic gains during the first three years of the single, nonrenewable four-year term to which Virginia uniquely limits its governors. He helped Webb oust Allen in 2006 and bankroll and campaign for a Democratic takeover of the state Senate in 2007, and was influential in 2008 making Barack Obama the first Democrat since 1964 to carry Virginia in a presidential race.
But in 2009, Kaine - moonlighting as Obama's hand-picked DNC chief - could not deliver a Democratic successor as Virginia Republicans ended an eight-year losing skid with sweeping victories for all three statewide offices.
And last year, the GOP won in another romp, negating the three U.S. House seats that Virginia Democrats captured in 2008.
Weeks before leaving office, Kaine proposed a $1 billion tax increase that even Democrats in Virginia's General Assembly rejected.
Still, he's the best shot the Democrats have at holding Webb's seat, said Mark Rozell, a political science professor at George Mason University in Fairfax.
"Webb really left the party in a dilemma, didn't he?" Rozell said.
"The question for Virginia Democrats is, 'Would Tim Kaine be their best candidate?'" he said. "It looks that way right now simply because he has the highest name identification."
"He did leave the governor's office without very high approval ratings and he wasn't able to leave a legacy by retaining the governorship for his own party," Rozell said.
Obama, with whom Kaine is close politically, has swayed Kaine's decision before.
The day after the 2008 election, Kaine flatly ruled out serving as national party chairman during a news conference. When Obama asked him a few weeks later to head the DNC, Kaine agreed. Since then, Kaine has often repeated his allegiance to the president.
Kaine has been mentioned for a cabinet seat should Obama win a second term. But keeping Webb's seat could also decide whether Democrats retain the Senate in 2012.
Should Kaine not run, the Democrats are not helpless, Brian Moran said.
"No, we don't have anyone who's run and won statewide besides the governor (Kaine), but remember that just five years ago, nobody even knew Jim Webb was a Democrat, much less that he would run for Senate," Moran said.
Webb was a Navy secretary under President Ronald Reagan, but switched parties and ran as a Democrat in 2006 in displeasure over then-President George W. Bush's handling of the economy and the Iraq War.
Bob Lewis has covered Virginia politics since 2000. Associated Press writer Ben Evans contributed in Washington.