To follow up on Monica Potts' post below, there's a simple explanation for why the Tea Party has gotten more unpopular over time: they're Republicans. What I mean by that is that at first, they worked hard to portray themselves as a movement that was above partisanship, just concerned with spending and critical of both parties. This was always baloney: their membership is almost entirely conservative Republicans. But that wasn't apparent to everyone, and the media often portrayed them in the way they wanted to be portrayed.
Then the 2010 campaign occurred, and both journalists and citizens saw the Tea Party purging Republicans in primaries for not being conservative enough. Then a whole bunch of Tea Party Republicans got elected, and since then, the (accurate) story of the budget debates has been about whether there's going to be some kind of a deal everyone can live with, or whether Tea Partiers are pulling the GOP so far to the right as to make a deal impossible.
So all of the news about the Tea Party in recent months has been not about this exciting new grassroots movement but about their role as a faction within the Republican Party. In that CNN poll, we see that only 10 percent of Democrats have a favorable view of them, while 71 percent have an unfavorable view. Among independents, the numbers are 31 percent favorable and 48 percent unfavorable, about what you'd expect for an extreme faction of one party (remember that most people who say they are independent actually lean toward one party; although they don't have data on this, I'd bet that nearly all the independents with a favorable view of the Tea Party are the Republican-leaning independents).
I'd argue that the idea that the Tea Party was ever something other than a bunch of conservative Republicans hoping to make the Republican Party more conservative was misconceived. But by now, no one believes that anymore, and so feelings about them have sorted out cleanly by party, pretty much as you'd expect.
