Tim Kaine is fighting back against what he calls false attacks.

Kaine, the likely Democratic candidate for U.S. Senate next year, is running ads on the Web and sending out fundraising appeals to counter a TV ad that accuses him of amassing massive debt while he was governor.

Several newspapers, as well as factcheck.org, have questioned aspects of the Crossroads GPS ad airing in Virginia that claims “Kaine’s reckless spending turned a budget surplus into a big deficit.’’

Kaine’s Web ads, which are running on Facebook and assorted other Websites, and fundraising letters target former governor George Allen, his likely GOP opponent next year, as well as Karl Rove, the strategist who started Crossroads GPS.

“George Allen and Karl Rove think that they can win this race by spending a lot of money on false attack ads,’’ Kaine wrote in an email to supporters Monday. “Together, let's prove that they're dead wrong.”

The Kaine campaign says supporters are responding to its efforts, and more ads and emails are on their way. 

“The negative and misleading attacks by Karl Rove's Crossroads GPS have only energized our supporters,’’ Kaine spokeswoman Brandi Hoffine said. “That's why we're stepping up our efforts to respond with the facts to this blatantly false advertising.”

The ads are part of a five-state campaign that will cost a total of $1.8 million, as the group is also targeting Democratic Senate hopefuls in Massachusetts, Missouri, Montana and Nebraska. More than $600,000 is being spent in Virginia.

In the Virginia ad, titled “Applause,” Crossroads looks to link President Obama’s economic record to that of Kaine’s when he had Virginia’s top job.

“Reckless spending, massive debt – no wonder Tim Kaine applauds Obama,” according to the ad.

As many newspapers and factcheck.org noted, Virginia law requires balanced budgets, so technically Kaine did not leave a “deficit” when he left the governorship in January 2010. His final proposed budget included cuts and a tax increase (that did not pass) to make up for a funding shortfall that stemmed from the worst economic downtown since the Great Depression.

  “The anti-Kaine ad alleges that as governor he took the state budget from surplus into deficit. That, of course, is impossible,’’ the Roanoke Times writes in an editorial. “The state must have a balanced budget.”

Kaine has been trying to use the attack ad to emphasis one of his key points for the 2012 campaign — that Kaine knows how to cut spending and balance a budget, while his opponents do not.