It appears Conway's best hope is to turn the spotlight on Paul and depict him as a man with extreme views, far outside the mainstream. The increased media attention on Paul’s more controversial statements has hurt his favorability numbers. From the PPP blog:
The more Kentucky voters get to know Rand Paul, the less they like him. When PPP first polled the race in December Paul's favorability was a +3 spread at 26/23. By May it was a -7 spread at 28/35. Now it's a -8 spread at 34/42. The national media attention Paul has received has hurt his cause with voters in the state--38% say it has made them less likely to support Paul while 29% say it has made them more inclined to vote for him and 33% say it hasn't had an impact on their attitude toward Paul one way or the other.
The fact that Democrat Conway is doing well in a Republican-leaning state in what is shaping up to be a good year for the GOP is a reminder that there is some truth to the old line, "All politics is local."