WASHINGTON (AP) — Instantly on the attack, allies of Republican leader Mitch McConnell launched a televised barrage against newly minted Democratic challenger Alison Lundergan Grimes in Kentucky’s high-stakes Senate race on Wednesday, a day after primaries in several states that also set up a Republican runoff in Georgia and left tea party insurgents still scratching for a breakthrough triumph.

Grimes countered with a new ad of her own, promising Kentucky’s voters, “no matter who the president is, I won’t answer to him, I’ll only answer to you.” It marked a quick attempt to neutralize McConnell’s assertion that she would serve as a rubber stamp for President Barack Obama.

The exchange underscored the president’s unpopularity in Kentucky, where a recent Courier-Journal Bluegrass poll of registered voters found that only 29 percent of those surveyed had a favorable opinion of him and 57 percent had an unfavorable one. McConnell’s ratings after 30 years in office are almost as bad, the poll said, 29 percent favorable and 49 percent unfavorable.

Kentucky and Georgia stand out as two of the most competitive races in the country this fall, at the center of a nationwide campaign in which Republicans are mounting a strong effort to gain six Senate seats and win a majority. Somewhat improbably, given the states’ strong Republican leanings, they also are the two where Democrats have their strongest hopes of winning seats currently in GOP hands and offsetting inevitable losses elsewhere.

Michelle Nunn, the easy winner of the Georgia Democratic nomination, campaigned in Atlanta on Wednesday and predicted the Republican runoff would be a “race to extremes and represents the acrimony and inflexibility that people are tired of already in Washington.”

Republicans David Perdue, a businessman, and veteran Rep. Jack Kingston, rivals in the 10-week runoff, previewed themes for the race ahead.

In a fundraising appeal after he finished first in the initial round of balloting, Perdue wrote, “Our outsider message clearly resonated in this election, and it’ll hold true in our head-to-head race.”

Kingston said if his own record as a lawmaker was fair game, so, too, was Perdue’s career as a businessman, including presiding over layoffs at Pillowtex, which manufactures sheets and other bedding. “My opponent says, ‘Trust me with America,”’ Kingston said Tuesday night after finishing second in the first round of voting. “What about those 8,000 Pillowtex employees who trusted their jobs to him and he fired them.”

The contests Tuesday across six states marked yet another series of high-profile setbacks for tea party groups and their allies who so far have failed to topple a single Republican incumbent this year. There are primaries ahead in Mississippi and Kansas where incumbent lawmakers face challenges from the right, and another ideologically tinged struggle is unfolding in Alaska, where Republicans seek a rival for Democratic Sen. Mark Begich.

McConnell’s triumph over challenger Matt Bevin in Kentucky marked the latest in a series of victories for a Republican establishment that was stung in 2010 and 2012. In both years, insurgents won primaries before seemingly winnable Senate races, in Nevada, Colorado, Missouri and Indiana, only to prove too conservative or undisciplined to prevail in November.

Party officials said the outcomes so far this year lessen chances the same thing will happen and increase their prospects for establishing a GOP Senate majority. For their part, vanquished challengers and their supporters claim to have pulled the already-conservative establishment rightward in the course of primary campaigns.

“Matt Bevin lost tonight, but his effort was not in vain as he has helped move conservatism forward and Sen. Mitch McConnell and the Republican Senate leadership to the right,” Drew Ryun of the Madison Project said as the Kentucky results rolled in. 

Democrats readily agreed that Republicans have been pulled rightward, and said it would disadvantage the GOP in key races where the overall battle for Senate control will be decided.

“In order to avoid losing to the tea party, Washington Republicans have embraced their candidates and policies. It’s a good strategy in the primaries, but one that forecasts defeat for Republicans in the general election this fall,” Democratic spokesman Justin Barasky said in a memo summarizing the Tuesday night primaries.

It’s a theory that will be tested as much in Kentucky as anywhere else.

McConnell used testimonials in his television advertising from fellow Kentucky Sen. Rand Paul, a tea party favorite, and spent more than $9 million of his own campaign funds to dispatch tea party-backed challenger Bevin.

The primary won, he shifted his focus to the fall campaign immediately, challenging Grimes to three debates “without an audience, without props and without notes.” She did not immediately respond.

At the same time, Kentuckians for Strong Leadership, a pro-McConnell group, launched a two-week air assault that says Grimes is backed by Obama’s allies from Hollywood and elsewhere. “Michelle Obama let the truth slip out at a new York City fundraiser, calling Grimes’ election critical to President Obama’s liberal agenda that’s hurting Kentucky,” it says.

An allied group, the Kentucky Opportunity Coalition, is slated to begin ads in two weeks — just after the current commercial stops running — and remain on the air until Aug. 27. The total cost is estimated at about $5 million, at a time when McConnell will be replenishing his own campaign coffers after the costly primary.