Top pollster Stanley Greenberg is not shy about criticizing the White House when he thinks it’s warranted, and his opinion is widely respected by Democrats in Congress. So if Greenberg tells moderate Senate Democrats that they vote against Obama’s jobs bill at their own peril, will they believe him?

In an interview with me this morning, Greenberg made a strong case that moderate Senate Democrats in red states would be foolish and shortsighted if they vote against the American Jobs Act today, as some of them appear to be prepared to do. The White House and Dems have been railing against Republicans for opposing the jobs bill, but if a few Senate Dems defect, and a simple majority of the Senate doesn’t support it, that will dilute the Dem message that Republicans are the key obstacle to progress on the economy.

But Greenberg’s case for voting for the bill went significantly beyond this concern about overall party messaging. He argued that moderate Democrats who vote against it are actually imperiling their own reelection chances.

“They reduce their risks for reelection by showing support for a jobs bill that’s going to be increasingly popular as voters learn more about it,” Greenberg said. “They have to be for something on the economy, and this the kind of proposal they should support. If I were advising them, I’d say you want to be backing a jobs bill with middle class tax cuts paid for by tax hikes on millionaires. Moderate voters in these states very much want to raise taxes on the wealthy to meet our obligations.”

Crucially, Greenberg pointed out that if moderate Dems are hoping to show distance from the President and his low approval numbers by voting against the jobs bill, they run another risk: Dem disunity on the economy could backfire on them.

“Voting No would increase their risk of losing,” Greenberg said bluntly. “Democrats would look divided on their central agenda. In the end you all go down with the ship here. Why would you send Democrats back to the Senate if they are divided on the most important issue facing people? Here you can show unity and purpose, which Democrats have not had an opportunity to do during budget negotiations.”

Greenberg dismissed concerns about Obama’s overall numbers. “It’s a long time until the election, and the presient’s standing can go up,” he said. “If the Democrats are divided and have a weak vote on the jobs bill, then moderates will only hurt themselves.”

One other separate point: As you may recall, Senate Dems complained vociferously for months that Obama had not used the bully pulpit effectively to rally support for his proposals. Well, now polls suggest that he has done just that. Yet that still hasn’t been enough to persuade some Senate Dems to maintain unity behind them. But as Greenberg notes, they follow that course at their own peril.