Something everyone seems to be forgetting- Ross Perot. His candidacy was based on two things: concern over the deficit, and concern over Clinton's trustworthiness. With Tsongas championing the deficit as his main issue, and lacking the adultery/draft-dodging scandals of Clinton, their will be little room for Perot in the race, and he might not bother. Does this mean that Tsongas takes Perot's voters+Clintons? I'm skeptical- even in spite of being more moderate and less scandal ridden then Clinton, his being from New England rather then the South and his lesser charisma would leave him less able to win over moderates and Southern bubbas.
Should he be elected, a stronger emphasis on deficit reduction then Clinton, definitely, as he was even more DLC then Clinton. Furthermore he wouldn't stumble so much as Clinton did early on and lose his political capital-he would be savvy enough to avoid the gays-in-the-military fumble, the backlash over absence of middle-class tax cuts(which Clinton promised but didn't deliver) and probably nominates less controversial people.
I can't find much about his specific economic proposal though. Presumably a portion of his deficit reduction strategy would be tax increases, and we would see greater military cuts then Clinton pushed through. Also, as he was more socially liberal, we probably see more leftwing supreme court nominees- Lawrence Tribe and so on.
As he dies in 1995, the sympathy vote and strong economy will carry his successor over the line(Gore or a Southern Governor I suspect so as to balance out the ticket geographically, but probably not Clinton). With the strength of the economy in 2000, successor is probably reelected(fun fact: would be the longest serving president since FDR).
With the Democrats having been in power for 8 years prior to 9/11, they will cop some flack for not preventing it(unless it doesn't occur for some reason) rather then the boost that Bush recieved. Couple this with the absence of the Bush tax cuts and likely continued low spending(due to Republicans having higher skepticism of spending proposals when Democrats propose them) which will mean a significantly lower debt but slightly weaker economy in 2004, and you have a recipe for a Republican victory.