Rand Paul leading in Kentucky poll

Senate Republican candidate Rand Paul appears to have survived a rough foray into national politics, showing a modest lead in his Kentucky race, according to a poll released Sunday. 

The GOP candidate, son of Rep. Ron Paul (R-Texas), holds a six-point lead -- 51 percent to 45 percent -- over Democrat Attorney General Jack Conway, about a week after making remarks about the 1964 Civil Rights Act, according to a Courier-Journal and WHAS11 Bluegrass Poll. 

The lead is within the poll's margin of error -- plus or minus 4.2 percentage points. Only 4 percent were undecided of the 569 likely voters polled by telephone, which was conducted May 25-27 by SurveyUSA. 

The winner of the race will take over the seat held since 1998 by retiring Republican Sen. Jim Bunning