A new NBC/Wall Street Journal poll out Wednesday suggests that in key swing states, President Obama’s ad campaigns against former Massachusetts governor Mitt Romney are working.

While nationally the two rivals are locked in a dead heat, in 12 expected battleground states — Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia, and Wisconsin — Obama leads by eight points in the survey.

So, what gives?

“The obvious conclusion here is that the negative TV ads pummeling Romney in the battleground states...are having an impact,” conclude NBC’s political unit in their “First Read” morning briefing.

The data in the NBC-WSJ poll certainly backs up that sentiment. A month ago in those same 12 swing states, Romney averaged a 36 percent favorable and 36 percent unfavorable rating. Now, he is at 30 percent favorable and 41 percent unfavorable. Attitudes about Romney’s business background, a target of numerous ads run by the pro-Obama Priorities USA Action super PAC, are more negative in swing states.

All of which suggests that, despite handwringing from national Democrats, there is evidence to suggest that the attacks on Romney’s career at Bain Capital are having some effect.

That’s despite the fact that Obama and his allies are being outspent by Romney and his allies on the air right now.

This chart shows how much the campaigns and supportive outside groups are spending in those 12 states, according to a Republican media buying source. (There was no ad spending in Michigan this week).

Pro-Obama groups are spending a little over $9 million this week while pro-Romney groups are spending about $12 million.

Notably, however, is that the bulk of the Democratic spending comes from Obama himself, whose campaign is spending nearly $8 million on ads this week. The rest comes from Priorities USA Action, which is spending about $1.2 million.

Romney’s campaign, on the other hand is spending a little under $3 million on ads while the rest of the GOP spending is spread out among a multitude of outside groups.

His super PAC, Restore Our Future, is spending about $4 million. The American Energy Alliance is spending $325,000 in Nevada to attack Obama’s energy policy. The Koch brothers-backed Americans for Prosperity is putting $2.85 million behind ads this week. Concerned Women for America, a social conservative group, is spending $2.14 million on anti-Obamacare ads.

That means Romney can save his own cash for later in the race. But for now, at least, Obama’s ad blitz appears to be doing damage.