WASHINGTON — Although polls show that the tax measure nearing the finish line in Congress is unpopular, Senate Majority Leader Mitch McConnell, R-Ky., predicted Sunday that it will ultimately prove a political winner.

By next fall, he predicted, Americans will already be feeling the effects of the revisions in the tax code, a version of which passed the Senate early Saturday.

Senate approval has moved President Donald Trump and the Republicans who control both houses of Congress close to being able to claim their first major legislative achievement of an era in which they control both ends of Pennsylvania Avenue.

“We think this will produce results, results we will certainly be able to talk to the American people about in the fall of 2018 and 2020 as well,” McConnell said on ABC’s “This Week.”

The 51-49 vote broke almost entirely along party lines, with only one Republican, Sen. Bob Corker of Tennessee, opposing the measure. That no Democrats in either house supported it shows that they are making another calculation, McConnell acknowledged.

“They decided it was important to them politically to oppose this tax measure and take it to the American people, and we’re prepared to do that,” McConnell said. “We think the country’s been underperforming and we believe this will get the country performing better.”

A Washington Post/ABC News poll in early November found that only one-third of Americans support the tax plan, while half oppose it. Six in 10 said the legislation’s tax cuts favor the rich.

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Most credible economic analyses say it also will add to the deficit. The nonpartisan Joint Committee on Taxation projected it would add $1 trillion to the deficit over a decade, disputing the insistence by Republicans that it would pay for itself through economic growth.

Although the legislation has not yet made it to Trump’s desk, the battle to control the political spin around it has already been fully engaged.

“This was barely dragged across the finish line on a party-line vote,” one opponent, Sen. Angus King, I-Maine, said on CBS’ “Face the Nation.” “We’re going to find some really stinky stuff in here that we didn’t know.”

But he added that Republicans will try to make sure that “anything good that happens in America in the next year, including good weather at the Super Bowl, is going to be attributed to this bill.”

Republicans expressed confidence that whatever differences there are between the House and Senate versions of the legislation can be worked out without much difficulty.

One potential complication arose Saturday, when Trump said he would consider setting the corporate tax rate at a higher level than the House and Senate have approved. The president indicated he might accept a 22 percent rate, which is two percentage points higher than in two versions of the bill that are headed to a conference committee.

Trump budget director Mick Mulvaney played down the significance of Trump’s comments.

“We’re happy with both of those numbers,” Mulvaney said on CBS. “If something small happens in conference that gets us across the finish line, we’ll look at it on a case-by-case basis. But I don’t think you’ll see any significant change in our position on the corporate taxes.”

Separately, both McConnell and Mulvaney predicted that there will be no government shutdown. The government is set to run out of funding on Friday.

“There’s a group of right-wingers in the House who say they want to shut the government down. There’s a group of Democrats who want to shut the government down over” extending protection to people who were brought to the country illegally as children, Mulvaney said. “And there’s a group of lawmakers from some of the hurricane states who want to shut the government down until they get what they want.”

“The spending system is broken when any little group can sort of hold the government hostage,” the budget director added. “We need to get beyond that. I think that we will. I don’t think you’ll see a government shutdown.”

McConnell was more definitive.

“There’s not going to be a government shutdown,” the Senate majority leader said. “It’s just not going to happen.”