A new Marquette Law School poll that’s generating lots of chatter today finds that Scott Walker and his most likely recall opponent, Tom Barrett, are in a dead heat, with Barrett edging Walker by 47-46 among registered Wisconsin voters.

The really important finding here, however, is that Walker’s approval rating, and his head to head numbers with Barrett, have not changed in months — if anything, they’re going down. And this is in spite of the fact that Walker and his allies have vastly outspent rivals in TV ads.

Charles Franklin, a political scientist and expert in Wisconsin politics who directs the Marquette poll, sends over some numbers.

In January, Walker’s job approval was 51 percent; in March, it was 50 percent; and this month, it's 47 percent.

In January, Walker was leading Barrett 50-44; in March, 47-45; and this month, he trails 46-47. (Among likely voters, Walker leads by a point; all of these findings suggest a mostly unchanging dead heat.)

“There’s been a great deal of advertising in the state, especially from the Walker campaign and Republican supporters, and we’ve seen virtually no movement in the Walker numbers,” Franklin tells me.

What’s particularly interesting here is that just yesterday, Walker announced he’d raised a staggering $13 million in three months for the recall fight. But even though he’s likely to outspend his Dem opponent in the home stretch, it’s unclear how much that will matter, because the numbers suggest ads are unlikely to move the needle much going forward.

This means the race is all going to come down to turnout — the one area where Dems and unions can match Walker in resources and organization, perhaps neutralizing Walker’s ad spending advantage, Franklin says.

“It won’t take much in voter turnout to tip the race either way,” Franklin says. “You can spend an awful lot of money on advertising and it would be unlikely to change many minds. But the advantages that Democrats and unions have traditionally had in the ground game is certainly an area where they can match Walker’s organization at the very least.”