Last night, President Obama and Eric Cantor exchanged harsh words over the debt ceiling, and on the Senate floor just now, Harry Reid uncorked a harsh attack on Cantor that suggests Dems are embarking on a new strategy: Isolating Cantor as the new public face of GOP intransigence.

Reid’s remarks are worth quoting at length:

Even Speaker Boehner and Minority Leader McConnell seem to understand the seriousness of the situation. They are willing to negotiate in good faith, which I appreciate, and the country apppreciates.

Meanwhile, House Majority Leader Eric Cantor has shown he couldn’t be at the table, and Republicans agree he shouldn’t be at the table. One Republican told Politico last night, “he lost a lot of credibility when he walked away from the table. It was childish.”

We had negotiations going here in a room a short jog from here, and he walked out on the meeting...It was childish. Another Republican said Cantor is putting himself first. He said: “He is all about Eric.” End of quote.

The time for personal gain and political posturing are over. It’s time to put our economy and our country first. The risks we face are simply too great. We don’t need to take my word for it. More than 300 respected business leaders wrote to Congress night before last to make it clear how serious this crisis really is.

Accounts of what happened last night vary, but the one thing they all agree upon is that Cantor played a lead role in telling the President that revenue increases simply aren’t going to happen, and that Obama didn’t react kindly to it. As Reid’s remarks suggest, Dems now seem to be seizing on this episode to elevate and isolate Cantor — who by many accounts is more adamantly opposed to revenue increases than even Boehner is — as the primary obstacle to compromise.

That’s why Reid is singling out Boehner and McConnell as operating “in good faith,” implicitly suggesting that Cantor isn’t, while simultaneously drawing attention to the grousing among anonymous Republicans that Cantor is damaging the GOP’s credibility and cause. According to one account, even Obama himself privately told Cantor that at this point he seems to be actively looking for ways to scuttle the possibility of compromise. The Dem message this morning is all about driving a wedge between Cantor on one side and Boehner and McConnell on the other by painting the latter two figures as the unlikely new faces of GOP reasonableness and flexibility.

But will divide and conquer work? The problem is that it’s unclear whether this damages Cantor in any meaningful way. It’s true that Cantor has taken a hammering from some commentators for refusing to budge on taxes. But Cantor has assigned himself the role of the GOP’s leading anti-tax warrior. If his intransigence on revenues is earning him high profile criticism from Beltway journalists and from the Senate Majority Leader and even the President, this will only turn him into more of a crusading anti-tax hero in some people’s eyes.

Either way, the harshness of Reid’s attack on Cantor doesn’t bode well for the likelihood of a deal.