Today, President Trump’s approval rating is around 40 percent, and it was in the mid-40s among likely voters fairly recently. In the Pew study, 39 percent of voters who had an unfavorable opinion of both parties approved of Mr. Trump’s performance, about the same as among other registered voters. So long as that’s true, it would be hard for Mr. Schultz to find a path to victory.

Would he help Trump?

It is too early to say which issues Mr. Schultz might emphasize on the campaign trail. It is also far too early to forecast the winner of the Democratic nomination. But if Mr. Schultz runs, it is easier to imagine how he could draw more votes from the Democratic candidate than from the president.

In principle, a strong centrist presidential bid shouldn’t draw more from Democrats than Republicans. And polls showed that Mr. Perot drew fairly evenly from Bill Clinton and Mr. Bush.

But Mr. Schultz said he had been “a lifelong Democrat.” Most of his views are aligned with the Democratic Party. More generally, fiscally moderate and centrist voters have trended toward Democrats during the Trump era. They represent a natural opportunity for the party in 2020. But it is a distinct possibility that Democrats will nominate a progressive candidate who isn’t well suited to winning voters from this group, and Mr. Schultz would be fairly well positioned to capitalize on their dissatisfaction.

Democrats also appear to have an opportunity among voters who backed a third-party candidate in 2016, and Mr. Schultz could presumably appeal to those voters as well. A Pew Research study in August found that voters who supported Gary Johnson or Jill Stein in 2016 had “cold” feelings toward President Trump by a margin of 84 percent to 12 percent. The exit polls found that self-reported 2016 minor-party voters supported Democrats in 2018 House races, 54 percent to 41 percent.

But Mr. Schultz could adopt a more conservative message focused on entitlements, the deficit or even political correctness. His most natural supporters would be underrepresented in many of the most important battleground states, like Michigan, Pennsylvania and Florida. And it is possible that Mr. Schultz’s presence in the race could make it easier for certain Democrats to run as populists; he could offer a more useful foil than the president.

All of this supposes that Mr. Schultz would manage to claim a significant share of the vote. This is certainly possible, given the resources at his disposal, but it’s not inevitable either. He enters with very little support or even name recognition, and deep opposition to the president will make many voters reluctant to support someone who isn’t thought to have a serious chance to win, particularly if the Democrats nominate a broadly acceptable candidate.

For now, it’s hard to imagine him helping Democrats consolidate voters who disapprove of President Trump. He seems likelier to divide them.