This morning, the Rove-founded Crossroads GPS released a new ad hammering Obama over spending and debt.

“He’s adding $4 billion in debt every day, borrowing from China for his spending,” says the ad, which is part of a $25 million buy in multiple swing states. “Tell Obama: Stop the spending.”

What’s interesting is that the new ad has given the Obama campaign an opening to launch a new attack on a target that Obama and his aides had been reluctant to mention by name: George W. Bush.

It it a centerpiece of the Obama message, of course, that Mitt Romney would return us to the policies that “got us into this mess,” i.e., those of Obama’s predecessor. But most of the time, Obama aides leave that claim vague, without directly targeting the Bush administration itself.

But the rich irony on display with the new Crossroads new ad — an attack operation founded by a leading official in the administration that ran up the deficit and left behind policies that have continued to inflate it for three years — has opened the door to a more direct attack on the real sources of the deficits that are now being blamed daily on Obama.

On a conference call with reporters just now, DNC spokesman Brad Woodhouse ripped into the ad, and linked it directly to Bush’s policies. “Karl Rove has got to be kidding the American people,” Woodhouse said. Woodhouse pointed out that Rove was “the brain” for an “administration that included a Veep who declared that deficits don’t matter,” and added that the ad is “laughable coming from someone who bears responsiblilty for the problems that we’re facing today.”

“Romney’s plan is modeled after the same policies,” Woodhouse said, noting that he would cut taxes on the rich further and continue wars Obama is winding down.

When Obama came into office, he inherited a $1.2 trillion deficit from the Bush adminstration. While Obama has certainly run up the deficit from there, the Center on Budget and Policy Priorities has found that some of the big drivers of projected future deficits are Bush policies — the Bush tax cuts, and the wars in Iraq and Afghanistan.

As Jamelle Bouie noted recently, Obama has been somewhat reluctant to directly mention Bush and directly link Romney to the former president, perhaps because of a desire to avoid appearing like he’s trying to transfer blame for the status quo to his predecessor. It’s unclear how directly Rove is associated with Crossroads these days. But it does seem like ads like this one should open the door to a real conversation about who’s really to blame for the deficit and which of the two current candidates for president is offering policies that have more in common with the ones that did so much to create it.