A new poll that shows Kentucky Sen. Mitch McConnell trailing his Democratic opponent raises questions about whether the Republican Minority Leader’s unpopularity in the Bluegrass State may jeopardize his seat in November.

McConnell trails Alison Lundergan Grimes by four points in the Bluegrass Poll, 46 percent to 42 percent, with a margin of error of three percentage points. It’s the second survey in a week to show him locked in a tight race with Grimes, Kentucky’s Secretary of State. A Rasmussen poll released Feb. 3 showed the two candidates in a dead heat.

November is nine months away, and McConnell remains the favorite. But there are distressing signs for the Republican leader. The new poll found that 60 percent of Kentuckians disapprove of the powerful five-term incumbent, compared to just 32 percent who approve of his performance in the Senate. That’s a shade worse than the ratings registered by President Barack Obama, who lost the state by 22 points in 2012.

Before McConnell can face Grimes, he must first fend off a primary challenge from tea party-backed Republican Matt Bevin. The poll bolsters the argument Bevin’s supporters have made for his candidacy: that McConnell’s long record in Washington and weakened status in the state make the insurgent the better bet to hold the seat for Republicans in November. Bevin “has got a better shot at winning the general,” says Matt Hoskins, the head of the Senate Conservative Fund, which has already spent about $1 million to boost the challenger.

Bevin’s campaign hailed the survey as proof of McConnell’s vulnerability. “It’s clear the voters of Kentucky are rejecting Mitch McConnell and his big-government record of voting for tax increases, amnesty, debt increases and bailouts,” says Bevin spokeswoman Rachel Semmel. “As Kentucky voters learn more about Matt Bevin and his conservative vision for America, our campaign’s momentum will continue to grow.”

Yet McConnell still looks likely to coast past Bevin. The new poll pegged his primary lead at 26 points, 55 percent to 29 percent. In Washington, where McConnell is regarded as an adept tactician, there is widespread frustration among the GOP establishment at the damage the primary challenge could inflict.

“The best advocates and our top resource for retaking the Senate are Republican senators, and there’s an opportunity cost of mindlessly primary-ing them for primary and profit sake, especially when you’re talking about a conservative leader as helpful to his colleagues and the cause as Mitch McConnell,” says Brad Dayspring, a spokesman for the National Republican Senatorial Committee. “Dollars now being spent in Kentucky could have been very helpful in pivotal battleground states where Democrats like Kay Hagan, Mary Landrieu, Mark Pryor and Mark Begich are clinging to their political lives.”

The NRSC, the Senate GOP’s campaign arm, has not yet made expenditures in Kentucky. But McConnell has a huge war chest and a powerful set of Republican allies, which—combined with the state’s conservative bent—will make it difficult to oust him in November. At this point in the campaign, Grimes has been able to dodge the spotlight, with a light public schedule and few policy specifics. In some ways Grimes, 35, presents a difficult target for McConnell, who trails among female voters. But while she is the daughter of a prominent local Democratic leader, Grimes remains little known in the state. Over the next nine months, McConnell’s allies will attempt to tie her to Obama’s positions on health care and coal, which remain deeply unpopular in Kentucky.

McConnell’s spokeswoman told the Louisville Courier-Journal that the campaign was “very comfortable about where this race stands.”

Write to Alex Altman at alex_altman@timemagazine.com.