(CNN) Vulnerable Democratic incumbents are betting that the Republican tax bill will be a political albatross in the 2018 midterm elections -- but it could be a risky gamble, strategists from both parties tell CNN.

Of 10 Senate Democrats up for re-election next year in states that President Donald Trump won in 2016, not one voted to support the GOP's legislative achievement. Likewise, not a single House Democrat backed the bill.

At-risk Democrats likely felt less political pressure because the legislation has polled poorly and the President's approval rating remains low. But Democrats from red states will still need to win over a share of Republican voters next year, many of whom view tax reform and the President favorably.

"There's no doubt Democrats have the wind at their back, but that doesn't mean that these red state Democrats are going to get a free pass on their votes," said Neil Newhouse, a Republican pollster and co-founder of Public Opinion Strategies. "The more these guys act and vote like national Democrats, the more they are putting their campaigns at risk in 2018."

Lauren Passalacqua, communications director for the Democratic Senatorial Campaign Committee, said Democrats "were eager to work on bipartisan reform" with their Republican counterparts, "but at the end of the day, Republicans simply weren't interested, and that's because this was never about the middle class -- it was about massive tax cuts for corporations and billionaires."

Democrats "have to do what is right for their state," Passalacqua maintained. "It was not a political calculus."

Most Senate Democrats laid down a marker on tax reform in August, when 45 of 48 senators signed a letter outlining conditions for their potential support — including that Republicans forgo reconciliation, a method that enabled them to pass the bill with a simple majority. That was an immediate nonstarter for Republicans, as Democrats knew.

But a trio of endangered senators had left the door open for discussions with Republicans: Heidi Heitkamp of North Dakota, Joe Donnelly of Indiana and Joe Manchin of West Virginia. The White House set about making its case to these potential swing votes; one senior White House official on Wednesday recalled "many an evening sitting around a conference table with Joe Manchin, trying to earn his support."

Leading the discussions were White House legislative affairs director Marc Short, National Economic Council Director Gary Cohn and even the President himself. They remained in discussions with Manchin until the Senate first approved its tax reform plan earlier this month, said Manchin's spokesman Jonathan Kott.

"They made a good faith effort," Kott said.

But all three Democrats ultimately opposed the bill, a decision that "had a lot more to do with politics than I think it really did about policy," the White House official said, citing "the polarizing environment" in American politics.

"I think they're going to have to explain to their voters why they didn't want to deliver tax relief for their citizens," the official added. "And I'm sorry that they didn't decide to join with us."

In an interview with Politico this week, Manchin lamented that he could not support the legislation, saying he "was an easy pickup," and speculating that "two, three other Democrats would have been easy pickups, if they had just made an effort."

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By "they," Manchin meant Senate Republican leaders, who did not join the White House in engaging with Democratic lawmakers — in part because Republicans hoped to pass their measure swiftly, but perhaps also as a political calculation.

Democrats privately disagree over whether that go-it-alone strategy will prove shrewd or shortsighted for Republicans, particularly in front-line Senate races next year.

"McConnell blew this," said one senior Democratic source, speaking of Senate Majority Leader Mitch McConnell. The source added: "He and Trump will regret not having any Democratic support on this."

But a Democratic Senate aide viewed the dynamic differently: "The best thing for Mitch McConnell is to pass this bill without Democrats, because he can spend next year saying Democrats didn't give Americans a tax cut," the aide said. "Politically, it's a cutthroat move."

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For now, Democrats appear to have the political advantage on tax reform. A CNN poll released this week showed oppositio n to the bill has grown during the past month, with 55 percent of Americans now opposing it. Just 33 percent support the GOP plan, even after an expensive public relations campaign by Republicans and groups aligned with them.

Still, McConnell told reporters Wednesday that the task of selling the reforms has only just begun for the GOP. And many Republicans believe public opinion will improve as the new law is implemented, leaving Democrats in a worse spot.

"As the tax plan takes effect, Democrats on the ballot in 2018 will be hard-pressed to explain why they voted against a law that is putting more money in families' pockets and boosting our economy," said Katie Martin, National Republican Senatorial Committee communications director.

If voters continue to oppose tax reform, Republicans will likely feel the most impact in the House, where the party will be defending 23 seats in districts that Hillary Clinton won. On the Senate side, only one front-line race is expected to feature a Republican incumbent who voted for tax reform: Sen. Dean Heller, in Nevada.

But the pendulum could swing in the other direction, to the disadvantage of Democrats — particularly those from red states.

Said Newhouse, "Some of these red state Democrats may a year from now regret their votes."