President Trump’s core supporters are happy that House Speaker Paul D. Ryan is retiring but say they are not ready for a full housecleaning in Congress, holding out hope that the rest of the Republican leadership team will see Mr. Ryan’s departure as a chance to do more to back Mr. Trump.

The supporters, who have braved insults from the media and taunts from friends and neighbors for backing Mr. Trump, say they have either forgiven him or aren’t bothered by his “playboy years.”

They are beginning to sound concerns over growing government spending and debt and now are worried that the president’s plans for Syria may stick the U.S. with a much-longer commitment to a foreign civil war than they expected out of their “America first” leader.

But Mr. Trump has delivered overall on the big promises he made to them in smashing the status quo in Washington, leaving Republican and Democratic operatives squealing, while pushing for his pro-business and traditional values agenda.

“I must say that given all the constraints and barriers that President Trump is dealing with, I am extremely pleased,” said Bob Harden, who was master of ceremonies at a Trump event in Florida in the final weeks of the presidential campaign. “I don’t know how he has the intestinal fortitude to battle every day. Given the mainstream media, the Democrats, and even given the party elite in the Republican Party, I think he has done a fantastic job.”

Eugene Delgaudio, who served as an alternate delegate from Virginia for Mr. Trump at the Republican National Convention, said the president is the “political grenade” for whom grass-roots activists had been longing.

“There is one man who has extended the advance of our traditional American moral leadership with strides unseen since I was 14 years old, and that man is Donald Trump,” Mr. Delgaudio said. “My eyesight is failing, but I can tell you I see victory with Donald Trump across the board.”

The glowing reviews come from a minority view in the country at large. Mr. Trump’s approval rating averages 40.2 percent while his disapproval rating is 54.2 percent, according to FiveThirtyEight.com. He has been underwater since February 2017 and hasn’t even approached positive territory in the months since.

But he remains popular among Republicans, scoring an 85 percent approval and 10 percent disapproval rating in the April Quinnipiac University Poll.

Indeed, it’s Republican leaders in Congress who seem to take the brunt of Republican voters’ disapproval.

“I really have a problem with the Republicans in Congress,” said Jeff Crouere, a radio host in Louisiana and 2016 Trump delegate. “I think they have really turned their back on the commitment to voters, and I think we are going to have a real problem getting people motivated to vote this fall.”

Many Trump backers share that sense of urgency. They worry that the president’s agenda could come to a grinding halt if Democrats win control of the House in the November elections.

“It is going to be slaughter for Republicans,” predicted Cody Knotts, a Trump backer who lives in West Point, New York.

The numbers appear to be trending that way. When voters are asked whether they plan to vote for a Republican or a Democrat for their member of Congress this year, Democrats are ahead.

Democrats are riding an elections winning streak that has handed them a U.S. Senate and a House seat in deep-red territory. They also have notched major victories in governors and state legislative elections.

Some of Mr. Trump’s supporters, though, remain optimistic about Republican chances. They say the Trump-loathing message Democrats are pushing isn’t powerful enough.

“I truly believe this blue wave isn’t coming,” Mr. Harden said. Democrats “stand for nothing.”

Whether optimistic or pessimistic about November, Mr. Trump’s backers say Republicans could strengthen their hand if Mr. Ryan and Senate Majority Leader Mitch McConnell do more to get behind the president’s agenda.

They also hope that whoever succeeds Mr. Ryan, who is vacating his seat, will be more in tune with Mr. Trump.

Matthew Jansen, a Trump backer from Pennsylvania who is running for the state legislature, said Mr. Ryan’s exit shows how the party is shifting away from the Wisconsin Republican’s “white collar” conservatism and more toward the “blue collar” conservatism popularized by Mr. Trump.

“I fully believe that leaning full right and letting the base run the Republican Party is the ticket to success, and that was not the Ryan viewpoint,” Mr. Jansen said.

Mr. Knotts put it more bluntly: “This man was completely out of touch with the people that voted for Donald Trump.”

The president’s supporters are angry at Mr. Ryan even though the speaker has wrangled votes in the House to repeal Obamacare, pass crackdowns on illegal immigration and sanctuary cities, build the border wall and approve the $1.5 trillion tax cut package. Of those, only the tax cuts made it through Mr. McConnell’s Senate unscathed.

Scott Jennings, a Republican Party strategist, said Mr. Ryan also delivered on the military funding boost that Mr. Trump demanded, as well as funding for anti-opioid efforts that Mr. Trump made a hallmark of his 2016 campaign.

“I could go on but, but I ask: What’s most important? For the speaker to be a clone in attitude or for the speaker to deliver results?” said Mr. Jennings, who worked in the George W. Bush White House.

Mr. Jennings also questioned Trump supporters’ anger at Attorney General Jeff Sessions, who was one of Mr. Trump’s first major backers during the campaign and who pioneered many of the immigration positions that the president has adopted.

Mr. Trump has been viciously critical of Mr. Sessions, saying he should have squelched the Russia investigation and should be doing more to pursue Trump targets from the 2016 campaign and the Obama administration.

Mr. Jennings, though, said Mr. Sessions is “operating within the confines of the law and of what his job requires — period.”

“He just plows forward implementing the president’s agenda day after day, and doing so in a way that is honorable, ethical and between the navigational beacons of the DOJ,” he said.

That tax cut remains one of Mr. Trump’s marquee legislative wins, alongside the Senate confirmation of Justice Neil M. Gorsuch to the Supreme Court.

Enthusiasm for the tax cuts was dulled in March, though, when Mr. Trump signed a $1.3 trillion deficit-busting spending bill that boosted the Pentagon but also injected a massive amount of money for domestic programs while limiting funds for the border wall.

“I wanted to see some real positive movement on the wall by this point, but the government works the way it works, and you just have to be happy that Hillary Clinton is not our president,” Mr. Jansen said.

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