Facing a spirited Republican primary challenge in Kentucky, Senate Minority Leader Mitch McConnell released a poll on Thursday that found he still has the support of more than two-thirds of GOP voters.

McConnell led Louisville businessman Matt Bevin, 68 percent to 21 percent, with 8 percent of voters undecided. Given the six-term incumbent’s superior name ID, his wide lead is not surprising.

But the internal poll offered the incumbent some encouraging numbers among the primary voters likely to be Bevin’s base. According to the campaign’s polling memo, the lead holds up across several several demographic segments of the party, including “very conservative” voters and “Tea Party Republicans.”

The poll of 600 likely Republican primary voters was conducted Aug. 18 to 20 and had a 4-point margin of error.

Even with a big early lead, the McConnell campaign has made it clear it is not taking any chances with Bevin. It has come out aggressively against the insurgent challenger on the airwaves.

The GOP primary winner will face Kentucky Secretary of State Alison Lundergan Grimes in what’s likely to be a competitive general election. The race is currently rated Republican Favored by Rothenberg Political Report/Roll Call.