House Democrats are girding themselves for a crucial stretch of primaries beginning Tuesday that could make or break their chances at a majority — and have party strategists worried they could blow some big opportunities.

Key battles in Pennsylvania and Nebraska, as well as contests in Oregon and Idaho, will get decided this week that could dramatically alter the contours of the House map. They’ll be followed in quick succession by elections in 20 other states over the coming month that will pit a number of establishment-favored Democrats against upstart challengers, with key races from California to Texas to Maine.

The biggest House contests on Tuesday come in suburban territory crucial to Democrats’ chances at retaking the House. Democrats will pick their nominees to face Rep. Brian Fitzpatrick (R-PA) and for another open seat near Philadelphia in Pennsylvania’s newly redrawn congressional map, and decide whether to give former Rep. Brad Ashford (D-NE) the right to a rematch after he lost a close election to Rep. Don Bacon (R-NE) in 2016.

Nebraska

Ashford is favored in his race against left-wing challenger and nonprofit executive Kara Eastman in Omaha. National Democrats are excited about his return — he overcame a terrible 2014 cycle to defeat a GOP incumbent and nearly held on last year against Bacon, another tough campaigner — and the Democratic Congressional Campaign Committee is backing his primary bid, the only one of this week’s races they’ve publicly stepped into. Eastman’s team argues her support of single-payer health insurance is an asset — “both Democrats and Republicans need health insurance,” campaign spokesperson Heather Aliano said, before arguing base enthusiasm matters — but national Democrats say if Eastman wins they might not have a shot at the seat, since a district where a number of jobs are dependent on insurance giants headquartered in the city.

Pennsylvania

The race Democrats are most concerned about is the Fitzpatrick race, where self-funding philanthropist Scott Wallace has moved back into the district after decades away, most recently living in the D.C. suburbs and South Africa. Wallace, a grandson of one of FDR’s vice presidents, has spent millions on the race and most expect him to defeat Navy veteran Rachel Reddick, a young former Republican.

And next door in the Allentown-based 7th District, strategists say an anti-immigration Democrat who’s out of step with many of the party’s priorities may be the favorite in a messy three-way primary against a more traditional Democratic candidate and a Bernie Sanders-backed pastor.

“We’re experiencing some of the challenges that come with high levels of enthusiasm — people jump in who have some problems in their background that raise concerns. Sometimes they’ll win and then we have to manage it,” said one Pennsylvania Democratic strategist.

Democrats mostly aren’t panicked by the prospect of a Wallace nomination in the suburban 1st district – but most say they’d prefer to have a young, female veteran running for the seat who hasn’t been gone as long rather than a self-funding candidate who hasn’t lived there in decades.

“I don’t necessarily think he’s weak [in the general election], but he has some baggage,” said Pennsylvania-based Democratic strategist Joe Corrigan, who is neutral in the race but predicted he’ll be the nominee after spending more than $2 million of his own money on the primary, much more than she’s spent. “Objectively it’s probably better to have a woman who’s a veteran but I don’t think it’s a write-off if we get Scott Wallace by any stretch of the imagination. He’s got a good campaign team around him and has a lot of local support. That said, a woman would be better.”

That might be generous — Cook Political Report House race handicapper David Wasserman called Wallace a “badly flawed candidate” in a recent article due to his long time away from the district and time living in one of South Africa’s toniest communities, and he’s faced criticism for late payments on hundreds of thousands of dollars in taxes in Maryland (he said he didn’t get the letter forwarded to him in South Africa, and immediately paid them off when he found out).

Wallace’s team pushed back on the attacks on his record, pointing out that Fitzpatrick also moved back into the district to run after leaving the FBI when his brother retired for the seat two years ago, while touting his self-funding ability.

“Voters know that Scott grew up in the district, moved for college and a career — just as Fitzpatrick did — and has always been tied to Bucks County and this district. And Scott has the resources to fight any attack, unlike any candidate who has run here in recent history,” Wallace adviser Jefrey Pollock told TPM.

Democrats are hopeful that a solid wave election could help obscure any candidate flaws in a district that Hillary Clinton narrowly won and President Obama carried twice. And they’re bullish that Wallace’s millions will allow him to define the race on his terms in the expensive media market, forcing Republicans to spend heavily to keep up. Republican outside groups have already reserved millions in Philadelphia, a sign they’re bracing for a cash onslaught.

But they admit that he’s going to have to find a way to explain to voters in the upscale district why he supports some tax increases while defending his own delay in tax payments. And they concede that the moderate Fitzpatrick is going to be a tough out in the swing district.

Democrats are much more bullish about their chances in a newly redrawn district centered on Allentown, which Clinton narrowly won and Obama comfortably carried twice. But many aren’t thrilled about a man who they think may win — Northampton County District Attorney John Morganelli (D), who has repeatedly praised President Trump and holds hardline immigration views that are completely out of step with the national party (Morganelli campaign spokesman Rich Wilkins says he supports a DACA fix and “his positions in the past on immigration have largely been based on his work in law enforcement.”)

He’s facing off against former Allentown city solicitor Susan Wild (D), who has more mainline Democratic views and who Democrats think would be a strong general election candidate as well, and Greg Edwards, an African American pastor backed by Bernie Sanders who strategists think doesn’t have as good a chance on Tuesday.

A recent public poll found all three leading their possible GOP foes, with Morganelli, possibly due to his high name identification, with the widest lead. But Republicans think local elected official Marty Nothstein, a former Olympic cyclist, could run a strong race if he wins the nomination.

Morganelli might not thrill Democrats given his views — and they invite a future primary challenge if he squeaks through on Tuesday. But while his possible nomination smarts for progressives, it’s unclear whether he’d be Democrats’ strongest chance at winning the seat.

“I think we’re going to wind up with Morganelli winning the primary, which sucks because he’s not really a Democrat, but him not really being a Democrat might help us in the general [election],” said Corrigan.