By James Oliphant

WASHINGTON (Reuters) - Republicans' loss of control of the U.S. House of Representatives leaves the party with a more conservative congressional caucus that is even more bound to President Donald Trump and more united around his provocative rhetoric and hardline agenda.

Although some moderate Republicans who remain in the House may view the result as an indictment of Trump's strategy of focusing relentlessly on illegal immigration in the final stretch of the campaign, they will be a small minority.

The Democrats fell short of a tidal wave of voter support that would have given them control of both chambers of Congress, but in the 435-member House they headed for a gain of around 30 to 35 seats, giving them their first majority in eight years.

Many Republicans who lost were moderates from suburban-heavy districts who tried to keep some distance from Trump and his rhetoric, but lost anyway. That leaves a shrunken core dominated by conservatives from rural areas whose constituents overwhelmingly support Trump.

In short, Trump will stay Trump. Although some Republicans may blame him for Tuesday's losses, they are unlikely to rebel, especially given that the party kept control of the Senate.

At a press conference at the White House on Wednesday, Trump took the unusual step of singling out for criticism Republicans who lost House races on Tuesday, arguing that if they had embraced his policies more they would have kept their seats.

It was a clear warning to the Republicans who remain in Congress to stand by the president.

Over the past two years, the president has shown little inclination to change his slash-and-burn style or turn conciliatory. He knows that he remains without question the most popular figure in his party.

Now, Trump begins his run for re-election in earnest, where he will make every effort to galvanize his base of passionate supporters.

That means that even in the face of stronger Democratic opposition, Trump is likely to advocate for his "America First" agenda that prioritizes hot-button issues, such as illegal immigration and trade protectionism. This, in turn, will accelerate his dramatic reshaping of a party that for decades was defined by fiscal, social and national security conservatism.

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Knowing that House Democrats will not approve funding for a wall along the U.S. border, for example, will not keep Trump from continuing to make it an issue. In fact, he may find it more politically effective to have House Democrats as a foil.

The surviving Republican members in the House, too, will have little interest in cooperating with the new Democratic majority, leaving Republican congressional power focused in the Senate and the government largely gridlocked.

“A Democratic House means that if the president wants to get things done, he’s going to have to work across the aisle," said Jason McGrath, a Democratic pollster in Chicago. "He hasn’t shown any inclination to do that, but it will be interesting to see if this is a moment he will want to govern rather than just make points.”

Addressing the media, Trump urged Democrats to propose legislation on issues such as national infrastructure program and reducing drug prices. "Come on, let me see what you have," he said.

SUBURBAN SHIFT

The shift in Congress has long-term implications for Republicans in districts that flipped Democratic on Tuesday and gives Democrats an opportunity to build on gains in once-reliably Republican suburbs where education levels and incomes are above the national average - and where skepticism of Trump runs deep.

The party already faced challenges in trying to grow beyond its base of middle-class Trump supporters, white men, and evangelicals. It has lost ground among women, suburban voters, voters with college degrees, while showing little ability to win over young and minority voters.

That will almost certainly continue if a shrinking congressional caucus paves the way for greater fealty to Trump.

In the Senate, centrist Democrats from states that Trump won in 2016 such as Joe Donnelly in Indiana, Claire McCaskill in Missouri, and Heidi Heitkamp in North Dakota, were replaced by conservative Republicans who may credit their victories to the president.

"We had tremendous success with the Senate," Trump said.

Moreover, Trump’s fiercest Republican critics in the Senate, Bob Corker and Jeff Flake, are retiring. So is Paul Ryan, the Republican speaker of the House who at times differed with the president’s tone, if not his policies.

All of it leaves Trump a more dominant force in the party than he was even two years ago. And Trump, who campaigned heavily in rural states, can point to those Senate wins as evidence he can still drive his voters to the polls.

LOW EXPECTATIONS

All year, Republicans have been clear-eyed about their potential losses in the House, and so likely will not view Tuesday's result as a warning sign the party needs to change its ways.

Historically, the party in power loses several seats during the first midterm election of a new president, particularly if his national job approval ratings are low.

Democrats lost 63 seats in 2010 with Barack Obama in the White House, handing control to the Republicans, who brought Obama’s agenda largely to a halt.

In the closing weeks of the election, Trump stoked fears over a caravan of migrants approaching the United States from Central America and warned of the threat from liberal “mobs” if Democrats won power, trying to stoke his base to the polls.

Several Republican candidates and advocacy groups such as the Congressional Leadership Fund joined in, concluding that the party’s economic message was not resonating. In two years, should economic growth slow, the party may not even have that argument.

With Congress expected to produce little in the way of meaningful legislation in coming months, Republican candidates in the next election cycle are likely to have few accomplishments to point to. A 2017 tax-cut law will be a distant memory.

Those Republican candidates who run for office with Trump at the top of the ticket will have a difficult time establishing their own political identities – and they may not want to, as U.S. presidents by and large win their second terms.

(Reporting by James Oliphant; Editing by Jason Szep and Tomasz Janowski)