While a popular talking point, his comments are putting congressional Republicans in an awkward position, since many feel that lowering tax rates for everyone, including the wealthy, would help spur the most economic growth.
Causing further confusion, Trump even raised the idea that tax rates could actually go up for the rich.
"I think the wealthy will be pretty much where they are," he told reporters on Wednesday. "If we can do that, we'd like it. If they have to go higher, they'll go higher, frankly. We're looking at the middle class and we're looking at jobs.
Later that day, the notion of raising taxes caught one of the main tax negotiators off guard. House Ways and Means Committee Chairman Kevin Brady was entering a meeting in the Capitol when reporters asked for his thoughts on Trump's statement.
"So, when was that?" the Texas Republican asked reporters, who then told him the comment was made just a couple hours earlier.
Brady continued: "So, um -- look -- my goal is to lower taxes on every American, if it's possible, help them keep more of what they earn, and encourage them to reinvest back in the local economy. So that continues to be my goal."
It's hardly the first time Trump has said he doesn't want tax reform to benefit the rich. Just last month, for instance, the billionaire quipped that his tax plan went against his own financial interests.
"I'm speaking against myself when I do this," he said to laughs.
Treasury Secretary Steven Mnuchin, explaining Trump's claim about the wealthy, said at a Politico event Thursday that even if the wealthy get a break in their income tax rates, they ultimately may not pay less because of expected eliminations of loopholes and other tax breaks that they take advantage of.
With so few details known about the plan, however, it's entirely unclear if the fine print of an actual tax reform bill will match Trump's rhetoric or anything else key Republicans are promising.
Still, Trump's comments broke through this week, and the idea of excluding the wealthy from tax benefits wasn't met with the same enthusiasm among some Republicans.
Many argued that if the goal of tax reform is to free up more money for the economy, it makes sense to lighten the tax burden on the rich, too, since they pay most of the country's taxes.
"If you say we're not going to have any tax cut for wealthy people, then you're really not going to have much of a tax cut, so you get less stimulus for the economy," said Sen. Rand Paul, R-Kentucky.
Sen. Pat Toomey, R-Pennsylvania, said there was "universal agreement" that tax reform should help the middle class, and "if along the way a relatively wealthy person manages to benefit from that, I, for one, am not going to lose any sleep at all."
"I hope we focus on creating more wealth for everybody, rather than who do we ... insist on not being able to benefit from this," he added, while speaking in a Senate finance committee hearing Thursday.
Others were less candid. While they shared the President's gusto for the middle class, they weren't so eager to go on the record saying rich people should get tax cuts, as well.
"I'm looking for economic growth, whatever produces that," said Republican Sen. Ron Johnson, when asked by CNN whether the wealthy should get tax cuts. "I'm not laying out any red lines, I'm not saying what I'm going to demand or who should or who shouldn't. We just got to grow our economy."
When posed the same question, Republican Sen. Jerry Moran of Kansas said he liked the President's statement and thought it helped position Republicans well on the issue in terms of messaging. "I want to see some things that help the economy grow," he said. "There needs to be a balance, but I think what the president said is helpful as we set the framework for what a tax bill should like."
Sen. Orrin Hatch, chairman of the Senate finance committee, quipped that he was "going to hold (the President) to it" when asked for his thoughts on Trump wanting to spare the wealthy from any tax breaks.
But he suggested the reality might look a little different, raising the point that there are other options besides an income tax cut that could help the wealthy.
"I don't know what it's going to be," said Hatch, who's a member of the "Big Six" group of negotiators that's working on tax reform. "But you know there are ways that you can really benefit the wealthy and some that will be incidental benefits, so we'll just have to see."
One of those options could be eliminating the estate tax
, which affects estates worth over $5.49 million that get handed down to heirs after a person passes. Proponents of the tax argue that it helps bring in billions in revenue, while opponents say it unfairly targets the wealthy.
The incidental benefits are a reason why Democrats, who have been demanding "not one penny" in tax cuts for the wealthy, have been skeptical of Trump's claim.
When the President met with House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer this week, the Democrats pushed back on the President's rhetoric, according to a source familiar with the meeting. They argued there were various elements the administration has so far backed that would still reduce taxes for the wealthy.
The source wouldn't get into specifics, but the morning after the meeting, Schumer zeroed in on the estate tax on the Senate floor.
"If the President's tax plan repeals or rolls back the estate tax, it will be clear that a lot of this benefits the very rich, contrary to all of his words."