Former President Donald J. Trump has big policy plans should he be re-elected, including mass deportation of undocumented immigrants and a supercharged crackdown against new migrants, tax breaks on tips and property taxes, expanded oil drilling on federal lands and the elimination of the Education Department.

A unified Republican government — the coveted trifecta of the Senate, House and White House — would make those goals easier to reach and help neutralize Democrats, who would no doubt try to stand in the way. And it would give Mr. Trump a free hand to install more conservative federal judges, including in the event of another vacancy on the already right-leaning Supreme Court, which has already granted him broad immunity from prosecution.

It is a lineup Republicans are counting on.

“We are going to grow the Republican majority in the House; we are going to take back the Senate and send Donald Trump back to the White House,” Speaker Mike Johnson assured the MAGA crowd on Sunday night at Mr. Trump’s invective-filled Madison Square Garden rally in New York.

That outcome is no sure thing, but it is a real possibility given the closeness of the battle for the House, the Republican edge in the fight for the Senate and Mr. Trump’s neck-and-neck race with Vice President Kamala Harris. It would open the door to a Republican push on legislation after two years of divided government has kept Congress focused on the basics of keeping federal agencies open and aid flowing to Ukraine.

After his election in 2016, Mr. Trump also had unified control of government for two years. But his lack of experience, coupled with the resistance of some top Republicans — including Speaker Paul D. Ryan of Wisconsin and Senator Mitch McConnell of Kentucky, the majority leader — limited his ability to get what he wanted out of Congress, particularly after an extended push to repeal the Affordable Care Act failed spectacularly.