Then, in the last paragraph, they explain it:
The nationwide telephone poll was taken March 28 through April 2, with 1,196 registered voters participating, including 510 Democratic primary voters and 323 Republican primary voters.
19% more of the participants in the poll are registered Democrats! Obama had a 47-42% lead over McCain from this poll, but 46% of the respondents were Democrats. That means if he got all of the Democrats polled to say they prefer him, then he only got 64 of the 363 non-aligned voters to say they'd vote for him. If 63% supported him (as they say earlier in the article), then he got about 50% of the non-aligned vote.
Regardless, having that big of a skew in the polled individuals is going to skew the results. Pollsters will tell you they "normalize" numbers to take out the inconsistancies, but a 20% difference is hard to normalize, or justify.
Considering the Times and CBS ran the poll I guess my surprise should be at the fact they released the numbers on who they polled.