Speaker Mike Johnson labored on Wednesday to overcome resistance in his own ranks to bringing up President Trump’s marquee domestic policy bill for a final vote in the House, as Republicans dismayed by Senate changes threatened to derail it.

The House was marching toward a test vote that would allow the bill to come to the floor for debate, but several conservative Republicans raised objections, suggesting that Mr. Johnson might lack the votes to move forward.

Facing tight margins in the House, he can only afford a small handful of defections on the measure, which would slash taxes by a total of $4.5 trillion, increase funding for defense and border security, and cut nearly $1 trillion from Medicaid with more reductions to food assistance for the poor.

As of midday, at least two Republicans had said they planned to vote against the procedural measure.

While Mr. Trump huddled with holdouts at the White House and Democrats and Republicans lawmakers battled over the merits of the bill on the House floor, Mr. Johnson and his leadership team projected confidence. Top Republicans insisted they could push the legislation across the finish line ahead of Mr. Trump’s July 4 deadline, especially given their previous success corralling disparate factions of Republicans to help secure initial passage of the bill in May.

“We’re going to pass this,” Representative Tom Emmer of Minnesota, the No. 3 House Republican, said. “It’s just a matter of when.”