House conservatives are cheering President Trump on in his desire for a government shutdown, saying they have his back in the standoff over border wall money.

Though party leaders have been reluctant to test the GOP’s strength, the conservatives insist they should vote on a bill containing $5 billion for wall funding in the House.

“Heck yeah — and I think it’ll pass,” said Rep. Jim Jordan, Ohio Republican. “We’re going to have the money for the wall — exactly what the president talked about.”

That optimism stands in contrast to other Republicans, who say they don’t think such a bill could pass — and point out that little has changed, votes-wise, from the summer, when they ducked holding a vote on the Homeland Security spending bill for fiscal 2019.

That bill is the key hurdle in a funding deal to avoid a partial government shutdown looming this weekend. Current funding for Homeland Security, the Justice Department and dozens of other departments and agencies is slated to expire Friday.

Congress left town last week without any discernible plan on how to avoid it, with both parties saying the ball is in Mr. Trump’s court.

Conservative rank-and-file members say the practical and symbolic importance of the wall can’t be overstated, and they’re prepared to follow Mr. Trump over the edge if necessary.

“If it turns into a shutdown, I’ll be the last one to blink,” said Rep. Steve King, Iowa Republican.

Conservatives say the House should send the Senate a funding bill with $5 billion for the wall — higher than the $1.3 billion Democratic leaders now say they’ll accept — and force Democrats to block it.

Rep. Warren Davidson, Ohio Republican, said House Republicans already have blown two chances this year to pass conservative border security bills spearheaded by GOP Rep. Robert Goodlatte, but he said it’s worth a third try.

“Only in the Canadian Football League do you punt on third down,” Mr. Davidson said. “In America, we run three plays before we punt, so I hope we run at least a third play before we bring out the punter.”

The House Freedom Caucus has taken an official position calling for the wall funding in any spending bill, giving the approximately 40-member conservative group significant sway in the closing days of the House’s GOP majority.

“We’re going to do exactly what we told the voters we were going to do,” said Mr. Jordan, a founding member of the group.

But House Democrats say they’re not budging, and many say that even the $1.3 billion figure that their leaders have offered for border security is too high.

If they uniformly oppose a funding bill, GOP leaders can afford no more than about 20 defections to get a package through the House.

Rep. Nancy Pelosi of California, the Democrats’ leader, says flatly that Republicans can’t muster the votes on their own.

“They do not have the votes to pass the president’s proposal, $5 billion, whatever it is, for the wall,” she told reporters. “The only obstacle is the president of the United States.”

She sparred with Mr. Trump over those claims in a White House summit last week, and conservatives say they want to hold a vote just to prove her wrong.

“Nancy kept saying to the president, ‘You don’t have the votes in the House.’ And it might be useful to say, ‘Yeah, we do,’ said Rep. Mike Simpson of Idaho, a senior member of the House Appropriations Committee. “Other than that, it’s not going anywhere in the Senate. So I mean ultimately, we got to have a plan. I don’t know what it is, and we’ll see.”

House Majority Leader Kevin McCarthy of California says he’s 100 percent confident he could garner the votes for $5 billion in wall funding if necessary.

But GOP leaders agreed with Mr. Simpson’s analysis that the real test is to get something through the more evenly divided Senate, where Democrats wield the threat of a filibuster.

“We can get the votes in the House to pass what’s necessary. The issue has always been what the Senate can or can’t do,” said House Majority Whip Steve Scalise of Louisiana. “Ultimately we want to get an agreement that can get to the president’s desk.”

Leaders also are competing to satisfy moderate GOP members who are more keen on avoiding a shutdown and appear more willing to budge.

Rep. Tom Reed, New York Republican, said there can be a dollar figure for border security between the lines that both sides have drawn.

“There’s been some prior votes out there where I think $4 billion, $20 billion over five years has been discussed,” Mr. Reed said recently on CNN. “And we’re talking even less than that. And we can get there.”

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