The White House insisted Tuesday that the $1 trillion spending bill includes money for 40 miles of border fencing, as President Trump sought to shore up Republican voters by saying the deal also lays the groundwork for rebuilding the military.

The president said there is “enough money to make a down payment on the border wall,” and said a $15 billion boost in defense spending — without having a dollar-for-dollar match in domestic spending — has set a new standard that will benefit Republicans and the Pentagon.

“This is what winning looks like,” Mr. Trump said.

Republicans bristled after Democrats declared victory on the spending bill Monday, saying they had won every major fight by keeping money flowing to Planned Parenthood and sanctuary cities, boosting spending for the National Endowment for the Arts, bailing out Puerto Rico’s troubled Medicaid system, expanding college aid for poor students and preserving the Environmental Protection Agency’s budget.

“We have more money now for the border than we’ve gotten in 10 years,” said Mr. Trump. “The Democrats didn’t tell you that. They forgot.”

Still, Democrats’ biggest win was preventing more money from going to Mr. Trump’s proposed border wall.

White House Budget Director Mick Mulvaney said Democrats oversold that claim.

While no walls will be built in new areas, the bill includes $341 million to upgrade 40 miles of existing fences and barriers, which the administration said paves the way for the full wall Mr. Trump is seeking.

“You can call it new wall, you can call it replacement, you can call it maintenance, call it whatever you want to. The president’s priority was to secure the southern border, and that’s what this does,” Mr. Mulvaney said.

He showed reporters a photo of a chain-link fence that he said would be replaced with a 20-foot steel wall, at a cost of $8.5 million per mile.

“That’s what we got in this deal, and that’s what Democrats don’t want you to know,” he said.

Mr. Mulvaney accused Democrats of souring the bipartisan deal by “spiking the ball” and crowing over their wins when the agreement was released Monday. Mr. Trump said Republican accomplishments “flew under the radar.”

The package is expected to win approval before a shutdown deadline Friday, when a one-week stopgap bill expires.

Mr. Trump seemed to throw a stink bomb into the deal Tuesday morning when he took to Twitter to blast the concessions Republicans made to Democrats.

“Our country needs a good ‘shutdown’ in September to fix mess!” he tweeted, adding that the Senate should consider eliminating the filibuster.

The White House and congressional Republican leaders spent the rest of the day trying to explain away the remark.

“We’ve got a long ways to go between now and September,” said House Speaker Paul D. Ryan, Wisconsin Republican, though he added that he shares the president’s frustration with the Senate filibuster.

Senators of both parties, though, said their ability to filibuster legislation isn’t going anywhere.

“That will not happen,” said Senate Majority Leader Mitch McConnell, the Kentucky Republican who eliminated the filibuster’s use against Supreme Court justices after Democrats excluded it for all other presidential appointments.

Democrats said Mr. Trump’s comments have poisoned negotiations and show that Republicans cannot resist shutdown showdowns.

“My hope [is] he’ll be a constructive force in the 2018 budget,” said Senate Minority Leader Charles E. Schumer, New York Democrat. “I don’t think threatening a shutdown is good for America.”

Mr. Mulvaney countered that Democrats are the ones pushing for a shutdown, figuring that either Republicans will cave to avoid such a scenario or take the blame.

The budget director said that by agreeing to the spending deal, Mr. Trump has “completely destroyed that narrative.”

Mr. Trump said that in addition to border fence money, he won several billion dollars for a health care fund for miners and extended a school choice program in the District of Columbia. He also prevented money for Obamacare payments from being included in the bill — though he has promised to make the “unauthorized” payments anyway.

The biggest administration win, though, was the $15 billion boost in military spending. The White House claimed another $6 billion increase in earlier spending bills for a total increase of $21 billion.

Mr. Trump said the military buildup shattered the Obama-era precedent that every dollar of new money for the Pentagon be matched with an extra dollar for domestic spending.

Mr. Ryan, the House speaker, called the parity break a “game-changer.”

“No longer are the needs of our military going to be held hostage to domestic spending,” Mr. Ryan said. “We broke this parity, and we think it’s a really important step in the right direction.”

Mr. Trump initially sought $30 billion in defense money and proposed deep cuts to cover the costs without ballooning the deficit. He won about half his request but did not win his cuts. Instead, Democrats managed to increase money for some of their priorities, leaving even deeper deficits.

Democrats also said they didn’t cave on parity. The extra defense money was included as one-time emergency war spending, meaning it was not part of the base budget that carries forward into next year.

“The baseline in 2018, as we go to the budget, is going to be equal like it has been,” Mr. Schumer said.

Congress is less than five months away from the deadline for the fiscal year 2018 spending bill, and Democrats already are laying down markers.

A handful of Democratic senators facing tough re-election bids next year took credit for miners’ health care money in the current bill but said they would demand more money for miners’ pensions in the next round.

“When is it their turn?” said Sen. Heidi Heitkamp, North Dakota Democrat.

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