It was a plan House G.O.P. leaders hoped would satisfy everyone in their party: With a special budget bill, they would bypass Democratic opposition and provide tens of billions for the Iran war while imposing new election restrictions President Trump has demanded.

Instead, a day after the leaders released the plan, which hews closely to a spending request the White House sent to Capitol Hill last month, it became clear it is a product that no one really likes.

The measure, which House G.O.P. leaders are hoping to pass through the filibuster-proof reconciliation process, would 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.

On Thursday, even as the House Budget Committee voted along party lines to advance the blueprint, it appeared that fissures over the measure were opening by the minute inside the Republican Party.

Chief among them was a growing divide between the House and Senate, where Republicans have long been more skeptical of the endeavor. It would be the third time in 18 months that the party has turned to reconciliation — a maneuver created to help reduce federal deficits — to muscle through key elements of their agenda.

Senator John Thune of South Dakota, the majority leader, said there were open questions among G.O.P. senators over whether “the juice” needed to try to push the measure through was “worth the squeeze,” given that it would ultimately deliver far less military funding than Mr. Trump originally asked for.