Braun Research (PDF) for CN|2 (6/6-6/8. Registered Voters. March poll in parentheses)
Steve Beshear (D): 51 (48)
David Williams (R): 30 (38)
Gatewood Galbraith (I): 6 (--)
Undecided: 14 (12)
The sample leans pretty heavily Democratic (60-36), but remember that party registration in Kentucky tends to be heavily Democratic, even if voters lean conservative in this red state. To reflect this, Braun also asked which party voters felt they felt "closer to" (registration status be damned). By that metric, Dems only led 45-42, which is actually closer to parity than the 2008 exit polls.
One of the big issues here is clearly the fact that Beshear, who avoided a contentious primary and shepherded his resources well, has the airwaves to himself right now. Not only did he run that excellent biographical ad posted above, he launched another ad this week on budgetary matters.
Another big issue, without question, is that Williams limped out of a contentious primary where he underperformed drastically against teabagger fave Phil Moffett. Williams, who parlayed a huge resources edge in the primary into a modest 48% plurality win, is having a hell of a time coalescing Republicans behind his bid. According to the poll, Williams only snags 58% of GOP supporters, while Beshear actually picks off one-fifth of Republicans.
Williams campaign has been a bit of a mess, with running mate (and Ag Commissioner) Richie Farmer helping out by getting caught up in a spending scandal, where he charged taxpayers $1500 for a stay in a hotel suite, when his home was about 20 miles away.
All this is hitting Williams at a time when Beshear is reasonably well-liked at home. The Braun/CN|2 poll puts Beshear's favorability numbers in the stratosphere (67/25), and finds rare near-parity on the right track/wrong track metric (40/41).
If those numbers are legit, and they hold, it is going to be very tough for Williams and Farmer to find an electoral path to victory in the Bluegrass State.