WASHINGTON — President Donald Trump's brief flirtation with Sen. Chuck Schumer and Rep. Nancy Pelosi is over — or at least on a break — and the president has his eyes on a new set of Democrats: business-minded moderates.

On Wednesday, Schumer joined other leading figures in his party in denouncing Trump's new tax plan as a giveaway to the wealthiest Americans. "This is 'wealth-fare,'" Schumer quipped on the Senate floor. "It’s little more than an across-the-board tax cut for America's millionaires and billionaires."

But Democrats say it will be hard for Schumer and Pelosi to hold their members in line in the face of a proposal that would slash tax rates for corporate titans and potentially many middle-class families alike, as the president seeks his first major legislative accomplishment.

"There is an opening to bring some of those moderate Democrats in," said Kristen Hawn, a political strategist and former aide to the centrist Blue Dog Coalition in the House.

Democratic votes give Trump at least the patina of bipartisanship and they also serve as a cudgel in his negotiations with the GOP. The threat: If Republicans oppose him, he can just sweeten the pot for Democrats and bring more of them on board to get what he needs.

The courtship is well under way. Trump invited Indiana Sen. Joe Donnelly, a Democrat facing a tough re-election bid in 2018, to ride aboard Air Force One to an Indianapolis rally touting the tax plan on Wednesday, and he asked several Democratic members of the tax-writing House Ways and Means Committee to the White House to discuss the outline on Tuesday.

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Donnelly, one of three Senate Democrats who declined to sign a letter to Trump laying out conditions for a bipartisan discussion of tax reform, said in an interview Wednesday night that he spoke to Trump at length about the tax reform plan and a possible boost in infrastructure spending that Democrats would like to see.

But Donnelly wasn't ready yet to commit his vote to the tax proposal. "I’m going to try to figure out what’s in it," he said.

Rewriting the tax code is a tough goal — it's been 31 years since the last major overhaul — and Trump has his work cut out for him in getting Republicans aligned behind his plan. Some will be wary of the overall price tag, while others may be reluctant to kill certain breaks that benefit allies in the business community or their constituents — for example, lawmakers from New York, California and other states where taxpayers get a deduction for the state and local taxes they pay.

Since it would take just three Republican defections to kill a tax bill in the Senate if Democrats were united in opposition, that's given some Democrats optimism that they'll have a chance to help shape legislation that would actually implement Trump's blueprint. They've been encouraged by Trump's work with Schumer and Pelosi on a bill that kept the government running, raised the debt limit and provided aid for victims of Hurricane Harvey, his frustration with Republican leaders' inability to pass his agenda, and his willingness to buck GOP orthodoxy in the interest of a deal.

President Donald Trump pauses during a meeting with, from left, Senate Majority Leader Mitch McConnell, R-Ky., Senate Minority Leader Chuck Schumer, D-N.Y., House Minority Leader Nancy Pelosi, D-Calif., and other Congressional leaders in the Oval Office of the White House on Sept. 6, 2017 in Washington. Evan Vucci / AP file

After meeting with Trump Tuesday, Rep. Brian Higgins, D-N.Y., concluded that the president wanted to play ball with Democrats on overhauling the tax code. "This is going to be a negotiation," Higgins told NBC News.

Most Democrats will find an array of reasons to vote against a Trump tax-cut bill if it reaches the floor: The income tax cuts aren't progressive enough; the elimination of the estate tax is a boon for the nation's wealthiest families; or they don't want to finance a corporate tax cut by adding to the nation's debt. But for reasons of both policy and politics, some moderate Democrats would rather find a way to get to "yes" than to "no."

"He'll peel off a few," Rep. Alcee Hastings, a liberal Florida Democrat, said of Trump's odds of winning moderate Democratic votes.

Of course, the devil's in the details — and Trump intentionally left many out. For example, he would reduce the number of individual income tax brackets from seven to three —12 percent, 25 percent and 35 percent — but didn't set the income levels at which each rate would take effect. And even then, the plan leaves room for a fourth bracket between 35 percent and the current top rate of 39.6 percent.

"I don't expect Democrats to say that GOP tax proposals are dead on arrival, but I expect a lot of skepticism," said Jim Kessler, senior vice president for policy at the centrist Democratic think tank Third Way.

"Many Democrats would like to see a lower corporate tax rate and help for the middle class," he added. "At the same time, they'll be looking at what it means for the deficit and whether top earners get too much of a break. It defies conventional wisdom, but Democrats have been guardians of fiscal responsibility since 1993 and that will weigh heavily in this debate."

Trump may be willing to deal to win Democratic votes — or at least show that he's willing to do so to keep Republicans in line.

"He's transactional," Higgins said. "That's not a criticism."