By pretty much any estimation, President Trump has had a very bad week.

New poll numbers show his approval rating has hit a second-term low. He is weighing whether to restart a bombing campaign in an unpopular war against Iran. Gas prices are high and inching higher heading into Memorial Day weekend. And his grip over Republican lawmakers is beginning to slip after he proposed a pair of deeply unpopular spending items, prompting an unusual revolt from the Senate.

When faced with such a backlash ahead of midterm elections, many politicians would pivot, redirecting their focus to issues they are on stronger footing with.

But Mr. Trump has decided to double down, presenting himself as politically all-powerful even in the face of indications that he is not.

Over the years, Mr. Trump has often appeared to have an air of invincibility. He survived assassination attempts and won re-election despite being under multiple criminal indictments. He has successfully exacted retribution on many a perceived enemy. Now, with less than three years left in office, he seems comfortable burning whatever political capital he has in order to leave his legacy, even if it drags his party down in the process.

Rather than abandoning his plan for a $1.8 billion fund to reward allies who claim they were persecuted by Democrats, Mr. Trump has defended the proposal, suggesting he could have used the taxpayer money to enrich himself.

“I gave up a lot of money in allowing the just announced Anti-Weaponization Fund to go forward. I could have settled my case, including the illegal release of my Tax Returns and the equally illegal BREAK IN of Mar-a-Lago, for an absolute fortune,” the president wrote on social media. “Instead, I am helping others, who were so badly abused by an evil, corrupt, and weaponized Biden Administration, receive, at long last, JUSTICE!”

His acting attorney general, Todd Blanche, also attempted to defend the plan in a hostile meeting with Senate Republicans.

Inside the room, Mr. Blanche came under withering questioning and criticism. Several Republicans spoke up to express worry that the fund would be used to provide money to people who had attacked police officers during the Jan. 6, 2021, assault on the Capitol and were later pardoned by Mr. Trump.

The meeting went so poorly for Mr. Blanche that party leaders scrapped planned votes on another of Mr. Trump’s top priorities: a $72 billion immigration crackdown measure lawmakers had planned to muscle through before Memorial Day.

“There’s a boiling point here,” said Sarah Binder, a professor of political science at George Washington University. “Of course, the boiling over, it’s in part because Trump doubles down. He rarely admits that maybe he needs to backtrack a little.”

Mr. Trump was also undeterred when another unpopular policy position — using taxpayer money to help fund security for his $400 million luxury ballroom on White House grounds — was met with backlash on Capitol Hill.

He said that without the $1 billion, the “White House won’t be a very secure place.” He called for the firing of the Senate parliamentarian, Elizabeth MacDonough, a nonpartisan official who ruled that approving the money would violate Senate rules.

“The Republicans allow the Elizabeth MacDonoughs of the World to stay in power, and brutalize us,” Mr. Trump complained.

Another dynamic at play in the Trump White House is a lack of dissenting voices to some of the president’s most extreme ideas.

In Mr. Trump’s first term, some of the president’s most radical ideas were checked by aides like John F. Kelly, the Trump White House’s longest-serving chief of staff; Jim Mattis, Mr. Trump’s first defense secretary; and Gary Cohn, an economic adviser.

But those men are long gone, and their positions have been filled mostly by people who are true believers.

Underscoring that point, Stephen Miller, the White House deputy chief of staff for policy, this week defended the so-called weaponization fund, even as critics called it a “slush fund” that could give payouts to Jan. 6 rioters.

“So many lives destroyed, so many livelihoods ruined, so many people who were deprived of their fundamental rights and freedoms as American citizens,” Mr. Miller said of the need for the fund, adding: “This settlement is just a small measure of the justice that they are owed.”

Mr. Trump has seemed unconcerned about whether these ideas are popular with voters, and has lamented openly that Democrats are likely to gain ground in the midterm elections. He has been most animated when discussing how he exacts vengeance on Republicans who criticize him.

At a political rally Friday in Rockland County, N.Y., Mr. Trump boasted about the recent victories in Republican primaries in which challengers he backed took out incumbent lawmakers who had crossed him.

“We knocked out a bad senator from Louisiana,” Mr. Trump said to cheers. “We knocked out everybody,” he added.

Left unsaid was that Mr. Trump needed the votes of the Republicans he opposed.

Ms. Binder said she took Mr. Trump at his word when he argued last year that he had little further use for Congress, a suggestion that he could enact most of his agenda by circumventing lawmakers. She said that the president was thinking in larger terms about continuing to control the G.O.P. after his presidency, and what kind of legacy, historically and physically, he could leave behind. She pointed to his push to build a triumphal arch in Washington.

“He’s focused on the arch. I think he’s focused on his own personal legacy. He’s focused on vengeance,” she said. “He doesn’t have a legislative agenda, so does he really need a Republican Senate?”