Rick Perry's presidential campaign is sinking fast while Herman Cain's is on the rise, according to a Washington Post-ABC News poll released Tuesday.

Mitt Romney remains in the lead with 25 percent of support among Republican voters, and Perry and Cain are tied at 16 percent. But the tie doesn't tell the whole story. Perry has dropped 13 percentage points since the last Washington Post-ABC News poll last month, while Cain has risen 12 percentage points. That puts Cain in a very strong position to overtake Perry.

The only other candidate with double-digit support is Ron Paul, with 11 percent. Michele Bachmann and Newt Gingrich have 7 percent each, and Rick Santorum and Jon Huntsman trail the pack with 2 percent and 1 percent, respectively.

The worst news for Perry is that his support has fallen precipitously even among his base. Only 10 percent of Tea Party supporters back him now, compared to 45 percent last month. And among conservatives, his support has dropped from 39 percent to 19 percent.

Cain Grabs Perry Voters

Nearly all of Perry's lost support has gone to Cain, who now has a plurality of Tea Party support: 30 percent, compared to 5 percent last month.

We hadn't seen that yet, but that is great news, Cain said when a Fox News interviewer asked him about the poll Tuesday morning. It says that the flavor of the week might have some substance. Black walnut isn't a flavor of the week.

His jab was aimed at Sarah Palin, who called Cain a flavor of the week after he pulled off an upset win in the Florida straw poll late last month.

The biggest factor in Perry's decline has been his debate performances. The most devastating was his indication in the recent debate in Orlando that he would support in-state tuition rates for the children of illegal immigrants, saying, If you say that we should not educate children who have come into our state for no other reason than they've been brought there by no fault of their own, I don't think you have a heart.

Perry got a huge amount of flak for that comment, and all of a sudden he had to counter allegations that he was soft on immigration.

Governor Perry is desperate to shift attention away from his liberal policies that encourage illegal immigration, a spokesman for Mitt Romney said, according to The Huffington Post.

There is still at least one wild card in the race: Chris Christie, the governor of New Jersey, who spent months shooting down pleas for him to run but is now apparently reconsidering. When the Washington Post-ABC News poll included him in the list of candidates, he got 10 percent, which doesn't put him anywhere close to the top tier.