There is good news in this volatile election year for Senate Republicans struggling to hold on to their seats: There is mounting evidence that voters are willing to support them even if they won’t back Donald Trump.

The bad news is that still may not be enough to save the Republican Senate majority.

New polls released in several battleground states this week show incumbent GOP senators consistently outperforming the Republican presidential nominee among general-election voters. But Trump’s unpopularity threatens to swallow that advantage.

The GOP currently enjoys a 54-seat Senate majority, but they are defending a dozen competitive seats, while Democrats are defending just two. A four-seat swing toward the Democrats would flip control of the Senate if Hillary Clinton were to beat Trump on Nov. 8.

Fresh national surveys following the party conventions show Clinton widening her lead over Trump into the double digits and leading him in swing states like New Hampshire, Pennsylvania, Michigan and Florida.

That math and the new polling are why Trump’s recent polling nosedive is triggering Klaxon horns in Republican circles around Washington.

In New Hampshire, Sen. Kelly Ayotte (R) does five percentage points better than Trump according to a poll released Thursday by WBUR-FM. But Trump is down by 15 points to Clinton, leaving Ayotte 10 points behind her Democratic foe, incumbent Gov. Maggie Hassan.

A Pennsylvania poll released Thursday by Franklin & Marshall College showed Sen. Pat Toomey down by 1 percentage point against Democratic challenger Katie McGinty. The same poll showed Trump behind Clinton by 11 points.

The results are sunnier for Republicans in Florida, where Clinton leads Trump by only six points — and Sen. Marco Rubio is leading his Democratic challengers by double digits, according to a new Suffolk University poll.

Together, the surveys paint a picture where Senate Republicans could run near-flawless campaigns and still get swamped in a Clinton landslide.

“If Trump is losing every purple and even red state by double digits, that’s clearly cause for concern,” said Josh Holmes, a former aide to Senate Majority Leader Mitch McConnell (R-Ky.) who now works as a political strategist.

Holmes said it is much too early to assume that will happen. And the National Republican Senatorial Campaign has spent a year preparing for the uncomfortable possibility — now reality — that their candidates would be sharing the ballot with a walking controversy magnet.

“Let’s face facts,” wrote Ward Baker, the NRSC’s executive director, in a September 2015 memo. “Trump says what’s on his mind and that’s a problem. Our candidates will have to spend full time defending him or condemning him if that continues. And, that’s a place we never, ever want to be.”

Nearly a year later, Baker said in an interview this week that the campaigns he oversees have been executing the strategy he laid out in that memo — “Run Your Own Race … Show Your Independence … Remember the Basics” — with notable success.

“Our Senate campaigns are not taking the bait,” he said.

But Baker’s earlier prediction has been dramatically realized: Congressional Republicans are barraged day in and day out with questions about whether they support or disavow Trump’s latest off-message remark or inflammatory tweet, with the controversy swirling around his attacks on the family of Capt. Humayun Khan, a Muslim-American Army officer killed in battle, standing as only the latest example.

The problem was illustrated this week as Ayotte and Sen. John McCain (Ariz.) disavowed Trump’s criticism of the Khans, only to get torched by Trump in a Washington Post interview. Neither senator has withdrawn their support for Trump’s presidential bid.

But Republican strategists believe that their Senate candidates can create some distance between themselves and the man at the top of the ticket by focusing on local issues.

In Arizona, McCain has been repeatedly drawn into Trump-related controversies — but he has also been relentlessly critical of Obamacare in a state where prices have spiked and several major insurers have opted not to sell policies on the federally mandated exchange.

In Nevada, Rep. Joe Heck, running to succeed five-term Democratic Sen. Harry Reid, has worked to establish a strong profile on water issues and solar energy regulations.

And in Ohio — in what may turn out to be the GOP’s biggest success story of the cycle — Sen. Rob Portman has combined a close focus on the state’s opioid drug epidemic and its sputtering coal industry with prodigious fundraising and an energetic field operation. That has him with a significant lead over his Democratic opponent, former Gov. Ted Strickland, in most public polls.

But Democratic operatives — with fresh memories of their own efforts to elect senators on an unfavorable playing field in 2012 — scoff at Republicans’ insistence they can “localize” Senate races in an increasingly nationalized political environment. They are determined to yoke every last GOP Senate candidate to Trump, and they are ready to unleash tens of millions of dollars worth of advertising to do so.

The Democratic Senatorial Campaign Committee on Thursday sought to preempt any attempts by Republican senators to steer clear of Trump, telegraphing their messaging strategy after Trump’s attacks on the Khan family dominated a week’s worth of news.

“[H]ere’s the plain reality for any Senators thinking that they can now create some distance between themselves and Trump: The damage is done,” the DSCC posted on Medium. “GOP Senators and candidates will be remembered for not having the guts to take a stand against Donald Trump and put their country over their party. And there’s nothing they can do at this point to change that perception.”

Democrats have other reasons to be bullish. For one, national Republicans do not appear to be making a major play for Colorado, where Sen. Michael Bennet (D) is seeking re-election. And an even bigger boost came last month when former Indiana Sen. Evan Bayh (D) announced he would seek a comeback, running for the seat being vacated by Republican Dan Coats.

Not only does Bayh give Democrats a candidate who has spent three decades appearing on Indiana ballots to contest a seat that had been expected to remain in GOP hands, but he also brings with him a campaign account flush with more than $9 million. Republicans believe Bayh is vulnerable, but they will be forced to shift significant resources from other competitive races to support their nominee, Rep. Todd Young.

“He’s going to have a thoroughly miserable three months,” Baker said of Bayh.

Still, Bayh’s entry helped Democrats offset Republicans’ own coup — convincing Rubio to seek re-election after pledging to move on to private life following his unsuccessful presidential campaign.

One Democratic strategist put the Indiana race among the three Senate seats most likely to flip from Republican to Democrat, joining Illinois and Wisconsin, where SensMark Kirk and Ron Johnson are seeking re-election, respectively.

The strategist, who spoke on the condition of anonymity to discuss internal party deliberations, said Democrats would need to pick up only one more seat among toss-up races in New Hampshire, Pennsylvania and Ohio — states that President Obama carried twice — assuming Nevada does not flip: “That’s a very, very big path to the majority for us.”

Democrats see other major opportunities in redder states like Arizona, Missouri and North Carolina where they hope to take advantage of a combination of weak incumbents, strong recruits and the Trump factor.

Republicans maintain that a Trump loss on the order of the 2012 Romney loss (4 points) or even the 2008 McCain loss (7 points) would still give them a good chance of keeping the Senate majority.

“If you substantially change the electorate so that you have a center-right coalition missing, then it becomes a problem,” Holmes said.

He also acknowledged other structural obstacles the GOP will have to overcome — including comparatively lackluster field operations for the Trump campaign and allies versus the Clinton campaign and the pro-Clinton Super PAC Priorities USA. Republican donors turned off by Trump — most notably the Koch network — have pledged to invest heavily in downballot races, but time is running out to reserve ad space ahead of Election Day.

Even if it were clear Trump was headed to a major loss, Holmes said, Republicans might have an opportunity to make an argument last deployed in 1996 to some success — “an excessive prosecuting for checks and balances on a Clinton administration.” The GOP picked up two Senate seats that year, even as Bill Clinton won in a 9-point landslide.

House Speaker Paul Ryan (R-Wis.) himself seems to have made a similar argument in a House GOP fundraising appeal sent on Thursday.

“If we fail to protect our majority in Congress, we could be handing President Hillary Clinton a blank check,” Ryan said in the National Republican Congressional Committee email, echoing the language used in 1996.

Correction: An earlier version of this article misreported that President Obama twice carried North Carolina. He carried the state in 2008 but not in 2012.