I'm not that surprised really. They've benefited from a pretty easy schedule most of the year, and this stretch is fairly brutal by NBA scheduling standards.
The two surprising factors:
1) They haven't figured out that Wade should be handling the ball at the end of games. LeBron is not as bad in the clutch as he has been this year, but he's not as good as Wade at attacking the basket and creating plays. He's always had a coach who doesn't know how to draw up a play for him and so settles on these LeBron-23-heave calls instead. They also both should be willing to pass to someone other than themselves (Chalmers or James Jones especially as good shooters). Oh and Bosh shouldn't be touching the ball at all unless he's in the post at that point in the game.
2) Their record against top 10 teams is something like 5-13, and this becomes a big deal. This isn't that surprising for an Eastern conference team to have a poor top 10 record, as other than Boston and Chicago, there aren't any East teams with winning records. The third best record is New York at 9-12. Even Orlando is 8-12. For comparisons, Atlanta checks in at 4-14, while Memphis, barely in the playoffs out West, is 12-13. Even if you expand out to the top 16, theoretically the playoff teams, it's still just Boston and Chicago (Orlando is .500).
What's surprising I suppose is that it is Miami doing this, after having supposedly been talking titles this year. To people who observed this skeptically, this looked like a high 50 win team and not much of a threat. They're more or less like LeBron's Cavs have always been: racking up double digit wins in the regular season against inferior teams, losing to quality teams. I still would not want to play them in a 7 game series if I'm, say, Boston, but Chicago is much scarier (and consider that this is basically the same Boston team that took 7 games to beat the Bulls two years ago in the first round, but smacked down the Heat after underachieving all last year). It's always been a Miami team this year that looked a lot like Orlando of the last couple years (for somewhat similar reasons, poor clutch play being one of them), should be good, will be scary to play, and will probably lose.
What they needed was either a) someone who can lock down the other team's playmaker, especially a point guard. or b) someone who can patrol the paint on defense and clear the boards. Since they've had neither, every team in the league that has a good power forward or center or point guard has beaten up on them.