WASHINGTON — For Mitch McConnell and fellow Senate Republicans, the push for a sweeping tax overhaul was never anything like the divisive internal party struggle that prevented repeal of the Affordable Care Act.

“All of my members, from Collins to Cruz, were just more comfortable with this issue,” Mr. McConnell, the Kentucky Republican and majority leader, said in an interview this weekend, referring to the centrist Susan Collins of Maine and the conservative Ted Cruz of Texas. “Everybody really wanted to get to yes. There was a widespread belief that this was just a good thing to do for the country and for us politically.”

Still, pulling off a victory in a contentious early Saturday morning vote took weeks of careful management of various unpredictable personalities — including President Trump and Senator John McCain of Arizona. It was a win that Democrats believe will come back to haunt Republicans because of the legislation’s emphasis on business and the affluent and its potential to explode the federal deficit.

Mr. McConnell said time would tell. “They are convinced it is good politics to be against it, and we believe it is good politics to do it,” he said. “We either get the growth rates or we don’t. In other words, one of these sides is going to be proven wrong.”