I suppose we shouldn’t be surprised by this. But even as it’s becoming official that Obama’s jobs bill in its current form is doomed in Congress, new polling shows that Obama is clearly winning the argument over it with the public.

Yes, Obama’s overall approval numbers are very bad. But today’s Washington Post poll finds that Obama has made big gains over Republicans on the specific question of who is more trusted to handle jobs. Obama has a 15 point edge on the issue, 49-34, up from a tie of 40-40 in early September.

That’s not all. The poll also finds that a majority, 52 percent, support Obama’s jobs bill, versus only 36 percent who oppose it. And 58 percent say it would improve the unemployment picture, versus only 39 percent who say it wouldn’t. Even more interesting, a whopping 70 percent say Republicans are more intested in protecting the interests of the wealthy than those of the middle class — while 52 percent say Obama protects the interests of the latter.

It gets more interesting. Despite the ubiquitous claims that Obama’s new populism is only about juicing the base, today’s poll shows strong support for Obama on jobs among moderates and independents, according to data provided by the Post polling team.

* A majority of moderates (53-27) and a plurality of independents (44-31) trust Obama more on jobs.

* A majority of moderates (52-34) and a plurality of independents (47-38) support Obama’s jobs plan.

* A majority of moderates (61-35) and of independents (52-44) say the jobs plan would improve the unemployment picture.

Post polling guru Peyton Craighill has the partisan breakdown in handy chart form and adds more analysis that you should check out. Je points out that the movement among independents is what has firmed up the turnaround for Obama on the jobs issue. If this doesn’t put an end to the ridiculous meme that Obama’s new populism is only about playing to Dems, then nothing will. In reality, this is also a bet about where the true middle of the country lies, and a bet that what indys want most is someone who will fight for them on jobs.

Again: You can’t sugarcoat the fact that Obama’s overall approval numbers on the economy are very bad, including among independents. But as today’s poll makes clear, those numbers are a referendum on the economy, and the failure to fix it so far — and not a referendum on his current policies, which have strong public support, even as they’re being blocked by Republicans.

As usual, even as Obama is persuading the public to back his plan, Democrats in the Senate announced today that it can’t pass in its current form. Worse, they said they’re not even sure that tweaking it — with a surtax on millionaires — can win unanimous Dem support. This, even though today’s Post poll finds that 75 percent — and 57 percent of Republicans — support hiking taxes on millionaires!

This is an old story, of course. Because red state Democrats seem to think they can’t possibly win an argument with Republicans over taxes, Dems are unable to unify behind proposals that have broad popular support. Maybe it’s true that fighting back against GOP attacks in red states is utterly hopeless. But even if these Dems are right about their own vulnerability, it doesn’t make the overall picture any less perverse.