Flush from last night’s victory, Harry Reid floated the possibility at a press conference this morning that Dems could revive the idea of a millionaire surtax when the talks begin over the year long payroll tax cut extension next year.

“I’ve talked to Senate Republicans, plural, who think there should be a fair tax on rich people,” Reid said. “I’m going to make sure that my conferees understand that this could be part of what we try to do.”

Given that Dems dropped the millionaire surtax during the talks over the payroll tax cut earlier this month, you’d be forgiven for concluding that Dems may not take it up again. But when it comes to paying for the year-long extension, the two parties remain far apart, and Republicans are going to push for still more spending cuts.

It wouldn’t hurt if Dems went into next year’s negotiations with a strong opening bid — i.e., a demand for a tiny surtax on a tiny minority of Americans (millionaires and billionaires) in order to pay for a modest tax cut for 160 million working Americans. After all, this skirmish may have weakened the Republican position on this issue — polls suggest that Obama and Dems effectively captured the moral high ground in this fight, and that the public has come to believe that Republicans favor the interests of the wealthy over those of the middle class.

More broadly, polls show that there’s been a clear shift in public attitudes towards tax fairness. Pew recently found that 57 percent of Americans now say the wealthy don’t pay enough in taxes, and 55 percent say the tax system is unfair. Whether that’s because of Occupy Wall Street, Obama’s jobs push, or the payroll tax cut fight, or some combination of them, is open to debate, but a shift has in fact taken place.

So another round of “class warfare” might be advisable for Dems to venture. After all, Republicans won’t hesitate from starting from a position that’s unacceptable to Democrats — more spending cuts and conditions attached to unemployment insurance, to name two. Republicans are now on record insisting that a full year extension is a must, and they’ve insisted that it be paid for. So why shouldn’t Dems stake out a hard line of their own?