Donald Trump, shown Tuesday during a town hall in Milwaukee, is viewed as a lightning rod for the House, with some observers saying that Democrats could make inroads by winning more seats. (Charles Rex Arbogast/AP)

It’s one of the most controversial things to say on Capitol Hill, sparking looks of shock and disbelief: The House majority is in play this fall.

For almost five years, ever since state legislatures and commissions finished drawing the new congressional districts for this decade, the Republican stranglehold on the House has been taken for granted because of the precise targeting that fortified GOP-held swing seats to seemingly withstand the toughest political climate. Even leading Democrats, just two months ago at their annual issues retreat in Baltimore, declined to predict anything close to winning the 30 seats they need in November to reclaim the majority.

Then Republicans started voting in their presidential primary, with Donald Trump taking a commanding lead.

By last week, as House Democrats showcased several dozen top recruits on Capitol Hill and at K Street fundraisers, the tone had finally begun to shift. Trump has become so unpopular among key constituencies, including the growing suburbs that are home to several dozen Republican members, that some independent analysts, political strategists and a few Democrats say that anything might be possible come Election Day.

“People are now beginning to understand that things could set up — could set up — to give us a shot at the majority. They’re beginning to understand that’s a possibility, because of Mr. Trump. But in any event, they understand we’re going to gain seats,” said Rep. Denny Heck (D-Wash.), who is helping lead the recruiting effort.

Donald Trump likes to speak for "everyone" and "everybody" – but we're not so sure these claims stand up. (Peter Stevenson/The Washington Post)

That’s a far cry from guaranteeing victory, but it’s quite a pivot from a Democratic caucus that four months ago unveiled a data-heavy effort dubbed “The Majority Project” that appeared to focus on winning back the majority by 2020 or 2022.

Republicans reject any hint that their majority could implode in the House, where Democrats hold their smallest share of seats since 1948. They contend that, even if a massive anti-Trump wave fully builds, Democrats recognized it too late. Filing deadlines have already passed in almost 40 percent of House districts, leaving many potentially ripe seats without a strong Democratic challenger.

“They’re missing candidates in the seats they need to win. The math is not on their side. Time is not on their side,” Katie Martin, spokeswoman for the National Republican Congressional Committee, said Tuesday.

Also, Republicans have reversed the financial edge the Democratic Congressional Campaign Committee held over the NRCC two years ago, opening up a $2 million advantage last month. Both sides say the Republican network of outside super PACs will swamp the amount of cash that Democratic super PACs devote to House races.

What is increasingly clear, however, is that the down-ballot effect of Trump or his leading rival for the nomination, Sen. Ted Cruz (R-Tex.), will no longer just focus on the Senate, which has long been viewed as a toss-up for who controls the majority next year. But in the House, Democrats are “headed for significant double-digit gains” unless Trump can alter his image, according to Nathan L. Gonzales, editor of the Rothenberg & Gonzales Political Report , an independent political analyst.

Such a big loss would leave Republicans holding the slimmest House majority either party has held in more than a decade. That could further destabilize the control of House Speaker Paul D. Ryan (R-Wis.) over a chamber in which his conservative flank has recently rebelled against his agenda.

Of the six most recent national polls, Trump has trailed the likely Democratic nominee, Hillary Clinton, by 10 percentage points or more in five of them.

Such a huge loss by the Republican presidential nominee would pit two oft-voiced truisms against one another: that the House majority is securely in GOP hands because of the tilted redistricting process in 2011, and that the era of voters splitting presidential tickets is over.

In the past 40 years, there have been three landslide presidential contests. Ronald Reagan’s massive victories in 1980 and 1984, by 10 and 18 percentage points, respectively, helped Republicans win 34, and then 16, seats in the House. In 2008, President Obama’s victory by more than seven percentage points helped Democrats win 21 seats.

Even under the currently drawn House map, Obama’s small victory in 2012 boosted Democrats to an eight-seat gain.

Then, a historically low 10 percent of voters cast ballots for their member of Congress different from the party affiliation of their presidential candidate. If the decline of ticket splitting holds, a landslide loss by a party’s presidential nominee would mean a disaster in the House.

“Now that it’s extremely likely that the Republican Party will nominate Donald Trump or Ted Cruz, congressional Republicans are entering uncharted and potentially dangerous territory,” Dave Wasserman, an independent House expert, recently wrote for the Cook Political Report.

The views of Wasserman and Gonzales crystallize the debate over Republican vulnerability in the House. Their handicapping reports rate an almost identical amount of Republican districts as vulnerable, but Wasserman takes a macro-view of the national environment, especially in an era in which four of the last five elections have produced big swings of at least 13 House seats.

Gonzales digs into district-by-district matchups and sees too many missing parts for Democrats. “Potential Democratic candidates who think an anti-Trump wave is developing either missed their opportunity or likely need to make up their minds soon,” he wrote in his most recent report.

Heck, chief recruiter for the DCCC, acknowledged that there are not enough Democrats with political surfboards — yet — to try to ride Trump’s wave to victory. “We’ve done very good, but not yet great. The process is still underway,” he said.

He conceded they have up to a dozen seats where “we’re taking a second look” but they still have some time to find a candidate. The focus is on districts with a highly educated populace, those in the suburbs and those with large numbers of Hispanic voters, or a combination of all three, because those are the voters most consistently offended by Trump’s message.

Three Republican seats in Minnesota surrounding the Twin Cities are now a target. Rep. Scott Garrett, a staunch conservative from northern New Jersey, faces a fresh challenge from a former speechwriter to Bill Clinton for a seat held by Republicans since Reagan’s first landslide.

After recruiting failures in western Colorado, with a large Hispanic population, the DCCC just got a call from a potential candidate who had initially spurned a challenge to Rep. Scott R. Tipton, who has won by comfortable margins since being swept into office during the Republican wave of 2010.

But, as is the case in many districts, time is of the essence. Filing deadlines in Colorado close in three weeks to mount a significant challenge to Tipton.

No one is guaranteeing a House takeover, but the Democrats finally have some optimism.

“There are going to be people that raise their right hand next January on our side of the aisle that nobody thought would be coming here,” Heck said.