House Republicans, already rattled by a special-election loss in Pennsylvania, are enlisting President Trump and other GOP leaders to help turn back a stronger-than-expected Democratic challenge in next week’s special election in a strongly Republican Arizona district.

Republican Debbie Lesko, a former state senator, faces Democrat Hiral Tipirneni, a physician and health-care advocate, in the April 24 contest to replace former congressman Trent Franks, who resigned last year after he reportedly offered to pay a female staff member $5 million if she would carry his child.

Starting earlier this month, Republican voters in the western Phoenix suburbs have received robo-calls in which Trump warns that “illegal immigrants will pour right over your border” if Democrats win the House. “Nancy Pelosi wants to send a liberal Democrat to Congress to represent you,” Trump says in the call. “We can’t have that.”

House Majority Leader Kevin McCarthy (R-Calif.) planned to travel to the congressional district on Thursday to help Lesko. House Speaker Paul D. Ryan (R-Wis.) raised money for the Republican nominee in the District on Wednesday.

The involvement of the president and GOP leadership underscores that no race is a surefire win for the party in an ­unforgiving midterm year, even one in a district where Trump prevailed by double digits in 2016 and Franks cruised to reelection. In a March special election, in a Pennsylvania district Trump won by double digits, Democrat Conor Lamb narrowly prevailed, unnerving a GOP fearful its House majority is in jeopardy in November’s midterm elections.

Republican groups have spent more than $500,000 to boost Lesko, efforts they say have helped her build a strong lead in absentee voting. According to state election officials, more than 128,000 ballots have been returned. Forty-nine percent of voters have been registered Republicans; 28 percent have been Democrats.

“When you look at the number of Republicans who’ve requested absentee ballots, I don’t know how you conclude that this is a race,” said Corry Bliss, the executive director of the Congressional Leadership Fund. “We’re spending $100,000 on digital and phones to ensure the highest possible number of Republicans return those ballots.”

At a closed-door meeting of House Republicans on Tuesday, the chair of the National Republican Congressional Committee gave lawmakers an upbeat assessment of the race, according to two people present.

Rep. Steve Stivers (R-Ohio) played down polls that showed a dead heat and said internal party numbers had Lesko ahead by high single digits or double digits, according to one of the attendees who spoke on the condition of anonymity to talk freely about the presentation.

Both attendees said Stivers emphasized that the early voting patterns were encouraging for Republicans in a race where the majority of ballots — perhaps as many as 80 percent — will be cast before the day of the election. Republican turnout, Stivers said, is running ahead of 2016, when Franks won by 37 percentage points and Trump won by 21 points.

However, both Republican and Democratic operatives agree the race has tightened. Tipirneni’s own polling has found her running stronger with Republicans and independents than Hillary Clinton did in 2016, keeping the race competitive. Like Lamb’s, Tipirneni’s campaign has focused largely on health care and benefits. According to election officials, the average age of voters who have returned ballots is 68 years old.

“Most of those voters live on Social Security and Medicare, and they love it,” said Rep. Ruben Gallego (D-Ariz.). “I know Debbie, I served with Debbie — her agenda that she had in the State House is not selling that well right now. With a wave year, it’s entirely possible that we do close the gap and Hiral wins.”

In debates, which wrapped up before the start of early voting, Lesko targeted Tipirneni for not supporting a wall on the U.S.-Mexico border and for opposing the Tax Cuts and Jobs Act. Tipirneni pivoted to health care, warning that Republicans were making coverage less affordable — a message many Democrats expect to use in the midterms.

“Debbie clearly has no health-care plan and seems to be okay with the things the administration has done to destabilize insurance markets even further, shooting premiums up,” Tipirneni said in an interview. “We all know that Speaker Ryan is proposing deep cuts in Social Security, Medicare and Medicaid to pay for the deficit that was created by the tax cuts.”

Democrats, who have not matched Republican investments in the race, are also watching closely to see how voters respond to Tipirneni’s health-care pitch. While stopping short of the universal Medicare pitch favored by the party’s left, Tipirneni advocated a plan that would allow anyone, of any age, to buy into Medicare, while letting Medicaid recipients opt for private insurance.

In debates, Lesko blurred the distinctions, accusing Tipirneni of favoring a “$32 trillion” health-care plan — the cost often cited for the health-care plan proposed by Sen. Bernie Sanders (I-Vt.) during the 2016 campaign.

“Hiral Tipirneni will be the first of many avowed single-payer supporters who lose this year because their progressive ideology fails to connect with people outside of the Democratic activist wing,” said NRCC spokesman Jesse Hunt.