Research 2000 for Daily Kos. 5/24-26. Likely voters. MoE 4% (5/10-12 results)
Rand Paul (R) 44 (42)
Jack Conway (D) 41 (39)
Paul 53/33 (56/27)
Conway 48/43 (46/44)
Paul's favorabilities are down among Independents -- from 62-16 to 58-20, and among Democrats -- from 37-45 to 29-57. Lucky for him, railing against the Civil Rights Act plays to his base. Among Republicans, Rand is now up to 79-9, from 76-10.
This race's big battleground will be independent voters -- Paul is currently winning them 42-31, with 27 percent undecided, and Democrats, where Conway is only getting 75 percent to Paul's 7 Percent, with 18 percent undecided. Remember, this is Kentucky, where a significant number of voters who vote Dem in statewide elections vote GOP for federal races. Paul has already consolidated GOP support, winning them 86-6, with just 8 percent undecided.
Update: I transcribed the poll results incorrectly in this post. Conway has 41 percent, per the poll, not 40.