House Republicans rushed to declare victory Wednesday following a narrow special-election victory in North Carolina, doubling down on a strategy of accusing Democrats of embracing socialism.

Despite holding the seat for more than 55 years, GOP leaders proclaimed that their win Tuesday validated their message of trying to tie every Democrat to a group of young, strident liberal Democrats and the most left-leaning presidential candidates.

“They do not want socialism,” Rep. Liz Cheney (R-Wyo.), the No. 3 member of GOP leadership, said of voters Wednesday. “They do not want to see their private health insurance taken away. They do not want to see illegal immigrants given free health care. They do not want to see the economy destroyed by the Green New Deal.”

That’s a risky bet for a party that continues to hemorrhage support in suburbs that serve as political cornerstones in swing states such as North Carolina, where Charlotte’s suburban voters on Tuesday continued to break against Republicans.

Voters in Mecklenburg County, a suburban stronghold, gave Democrat Dan McCready a margin of 12 percentage points over Republican Dan Bishop, bigger than the nine-point advantage McCready posted there during last year’s invalidated race in the state’s 9th Congressional District.

Bishop won the race based on running up the count in the more exurban and rural portions of the district in the south-central part of the state, continuing the geographical divide in the era of President Trump. That provided a sigh of relief for Republicans worried that defeat would have prompted even more retirement announcements.

But Democrats see the trend going deeply in their favor — in 2016, Republicans won this seat by more than 17 percentage points. “They needed to win it, they squeaked by. I don’t think any Republican in the House, who’s concerned about his or her electoral prospects, can feel better about the situation,” Rep. Hakeem Jeffries (N.Y.), chairman of the House Democratic Caucus, told reporters.

Democrats can still play offense in 2020, as at least 25 Republicans still in office won by less than 5 percentage points last year, including a handful who have already decided not to run again in 2020. History falls on the Democratic side, as the House majority has not changed hands during a presidential election year since 1952.

Republicans face a conundrum if they are going to try to win back the net gain of 19 seats they need to reclaim the majority. Many of those seats look more like the suburban portions of Mecklenberg County than they do Union County, a rural county along the state border that gave the GOP candidate 60 percent of its vote.

The party’s current messaging focus — heavily reliant on disparaging Rep. Alexandria Ocasio-Cortez (D-N.Y.), along with her “squad” of liberal freshmen — is resonating in rural areas that, for the most part, Republicans already hold.

Democrats went through a similar dilemma eight years ago, in their first months of being kicked into the minority after the GOP landslide of the 2010 midterm elections. In May 2011, Democrats won a special election in Upstate New York, taking a swing-seat district from Republicans with a singularly focused message.

Then, Democrats hammered away at the proposal to create premium accounts for Medicare by Paul D. Ryan (R-Wis.), then the chairman of the House Budget Committee. They accused the GOP candidate of wanting to “end Medicare as we know it,” and in a district that had a large elderly population, it resonated.

After their victory, Democrats promised to take that message all the way to the majority in the 2012 general elections.

“It sends a clear message that will echo nationwide,” said Rep. Nancy Pelosi (D-Calif.), then the minority leader.

By August 2012, that message had fizzled. Ryan wasn’t even politically toxic — GOP presidential nominee Mitt Romney chose him as his running mate. Their ticket lost, largely because of President Barack Obama’s incumbency and not Ryan’s budget proposals.

Republicans retained a healthy House majority, and by October 2015, Ryan became House speaker.

That May 2011 message, which Republicans called “Mediscare,” worked briefly but did not hold up over the long haul, as GOP candidates over time learned how to counter the attacks or at least neutralize them.

Democrats who have some rural constituents have another 14 months to learn how to deflect the Republican attack line on socialism before they face voters again. Republicans have the time to figure out how to make that message connect with more suburban voters or find another message. Some GOP leaders say it will work.

“I think it is scaring an awful lot of folks in those swing districts, scaring a lot of moderate Democrats and energizing a lot of our folks,” Cheney said.

House Minority Leader Kevin McCarthy (R-Calif.) suggested that there might be a narrow-enough path for his candidates to run entirely in sync with Trump during his reelection and eke out the House majority.

“The seats that we have to go win are not so suburban,” McCarthy told reporters, noting that there are 31 Democrats in districts that Trump won in 2016. “I think Trump’s going to carry them and more. And the difference is the Democrats now have a record.”

In what McCarthy called the “new socialist Democrat Party,” Pelosi has emerged as a “moderate” compared with the more liberal faction.

“I think they’ve got real problems,” McCarthy said.

In that regard, GOP leaders today sound somewhat like Pelosi in May 2011. At a news conference two days after that Democratic victory, Pelosi used the word “Medicare” 22 times, and throughout that summer she stuck to that message.

When asked how Democrats could win back the majority, she replied: “Medicare, Medicare, Medicare.”

It took several more election cycles for Democrats to pull together a message that connected with suburban voters and vaulted them into the majority.