House Republicans on Wednesday won narrow approval of their $95 billion budget plan to fund the war with Iran and impose new election restrictions President Trump has demanded, muscling through dissent in their ranks to send the measure to a skeptical Senate.

The blueprint would pave the way for filibuster-proof legislation known as a reconciliation bill that would bypass Democratic opposition and provide up to $73 billion in additional military funding, $12 billion for farmers and $10 billion to enforce severe new voting restrictions championed by Mr. Trump.

It was approved in a 216-to-214 vote, with all but two Republicans in favor despite considerable concern in their ranks about its cost, its scope and voting to fund an unpopular war just months before the midterm elections.

The plan faces an uphill fight in the Senate, where the Republican leader has cast doubt on his chamber’s willingness to embrace it.

The debate featured little in the way of direct discussion about the war with Iran, for which the bulk of the money is intended.

Speaking at length on the House floor in support of the plan, Representative Jodey Arrington, Republican of Texas and the chairman of the Budget Committee, described the effort as “supporting our troops in their time of need.”

“Just base-line battlefield readiness,” Mr. Arrington said. “Bullets and bombs to finish the job, and to come home safely and victoriously.”

Representative Mike Rogers of Alabama, the chairman of the Armed Services Committee, also omitted any mention of Iran, though he alluded to the conflict.

“No matter how you feel about the current events, these funds are necessary to ensure our fighting forces remain ready, our troops are paid and our nation is safe,” he said.

In the days leading up to the House vote, various Republican factions had quietly voiced grievances about the resolution. Budget hawks objected to the fact that none of the new spending would be offset by new cuts. Defense hawks said their party should use reconciliation to provide even more money to the Pentagon. Center-leaning House Republicans facing competitive re-election races were skittish about voting to fund a war that has driven costs up.

But as with most legislative initiatives that Mr. Trump demands, there was a sense of inevitability in the House about adopting the blueprint, and in the end, most would-be defectors swallowed their objections and fell in line.

In the end, only two Republicans, Representatives Thomas Massie of Kentucky and Warren Davidson of Ohio, and one independent who aligns with the G.O.P., Representative Kevin Kiley of California, voted no.

Fiscal hard-liners said they were willing to add $95 billion in spending in exchange for a promise that the reconciliation measure would eventually include new voting restrictions that would require people to prove they are citizens when they register to vote, impose strict new identification requirements for voting and severely curb voting by mail.

The blueprint hews closely to an emergency spending request the White House sent Congress in June to provide more money primarily for the Pentagon. Republicans have sought to fund it through reconciliation, legislation that is not subject to a filibuster because nearly all Democrats have said they are opposed to the war and will not vote to allocate money for it. In the Senate, spending bills typically need bipartisan support — 60 votes — to advance.

Representative Hakeem Jeffries of New York, the Democratic leader, called the legislation an “America Last Republican budget that will provide billions of additional dollars to Operation Epic Fury in the Middle East, which has been a complete and total disaster for the American people.”

It would be the third time in 18 months that the party has turned to reconciliation — a maneuver created to make it easier to pass bills that reduce federal deficits — to push through major elements of their agenda.

Yet it was far from clear that the budget blueprint would gain traction in the Senate.

Senator John Thune, Republican of South Dakota and the majority leader, suggested at a news conference on Tuesday that the Senate would “hold” the House’s budget resolution — not acting on it immediately but keeping it available — until he was sure the Senate could move a stopgap funding bill to avert a government shutdown at the end of September.

“It’s a possibility that, if necessary, we could pull that budget resolution passed by the House and use it to fund the government,” Mr. Thune said.

Even before that, a number of Republicans in the Senate had questioned the plan’s viability. Senator Roger Wicker of Mississippi, the chairman of the Armed Services Committee, has said he opposes it because it does not provide the Pentagon with enough money. Mr. Wicker has said he wants to ensure the military receives the full $1.5 trillion in funding Mr. Trump included in his budget request.

Senators Lisa Murkowski of Alaska and Thom Tillis of North Carolina both oppose the inclusion of the voting restrictions, known as the SAVE Act. Many Republican senators doubt that the measure will be allowed to remain in the reconciliation bill, which is subject to strict rules requiring that all provisions make direct changes to spending or revenue.

And Ms. Murkowski signaled she was wary that the Trump administration might interpret a vote in support of supplemental war funding as a vote by Congress authorizing the conflict with Iran. The president has not sought such authorization, and lawmakers in both parties have voted to require it.

In a hearing on Tuesday before the Appropriations Committee, Ms. Murkowski asked Defense Secretary Pete Hegseth whether he believed that a vote on “funding alone can substitute for explicit congressional authorization.”

Mr. Hegseth said he would defer to his legal team.