Former Florida Gov. Jeb Bush waves to the crowd as he formally joins the race for president with a speech at Miami Dade College, Monday, June 15, 2015, in Miami. (AP Photo/David Goldman)

In 2012, Republican presidential candidate Mitt Romney ran on a plan to cut income tax rates for the highest earners and for corporations. Sixty percent of voters disagreed with him, saying rates should — at a minimum — go up on people earning $250,000 a year or more.

And that difference showed up at the polls. Fifty-five percent of voters said the U.S. economic system favors the wealthy, with Romney losing that group by 45 percentage points. A majority said Romney's policies would mostly help those wealthy people; Romney lost that group by nearly 9 to 1.

These numbers may matter for Jeb Bush, because his new tax plan, unveiled late Tuesday, includes a lot of the same ideas that Democrats hammered Romney for.

Bush, like Romney, wants to cut the top rate to 28 percent, from the current 39.6 percent. Romney wanted to cut the corporate rate to 25 percent, and now Bush wants to cut it to 20. Romney wanted to end the estate tax and the alternative minimum tax, which almost exclusively affect higher-income earners. So does Bush.

Both plans proposed to limit tax deductions for the highest earners as a way of reducing their gains from tax cuts - and the effects on the federal budget deficit.

In the end, though, independent analysts found Romney's plan would have given a substantial tax cut to the wealthy. Bush's appears likely to do that, too.

But the plans also diverge in a few ways. Bush proposes half as many total tax brackets as Romney did, a move that pleases supply-side conservatives who want the smallest number of brackets possible.

In a nod to so-called Reform Conservatives, who are pushing Republicans to target more policies to help the poor and the middle class, Bush would double the standard deduction for all taxpayers and expand the Earned Income Tax Credit, which helps low-income workers.

For conservative populists, Bush says he'll end a tax loophole that allows investment fund managers to pay lower rates on much of their income.

Bush's challenge will be convincing voters that those changes represent a fundamental, rather than an incremental, improvement on Romney's tax plan. That could be a tough sell, both in the GOP primary and, if he gets there, the general election.

In the primary, most of Bush's rivals have sketched tax plans that cut rates far deeper than Romney would have.

With the encouragement of supply-side stalwarts led by economist Arthur Laffer, and to the delight of Democratic political hands, several Republican contenders have proposed flat taxes that would lower top rates dramatically. (The notable exception to that is the current GOP front-runner, Donald Trump, who has indicated a willingness to raise taxes on the rich.)

"Tax cutting is now fundamental to the GOP message and every candidate from Bush to Rubio, to Rand Paul, to (Chris) Christie and (Mike) Huckabee and (John) Kasich, (Rick) Perry and Carly Fiorina, is on the supply side tax-rate-cutting message," said Stephen Moore, an economist who has worked with Laffer to push candidates in that direction.

Bush's plan, Moore said, is "a good solid growth plan, but it may not have the sex appeal with GOP voters that a flat tax or a national sales does."

For swing voters in a general election, Bush may need to make the case that his plan lives up to his own lofty rhetoric.

In Detroit in February, he lamented that "Americans across the country are frustrated. They see only a small portion of the population riding the economy’s 'up' escalator." He declared, “the opportunity gap is the defining issue of our time.” He promised more details on how to close that gap.

Many of those details are in this tax plan. They flow from the idea that a simpler code with fewer loopholes could help working-class Americans find better jobs in a faster-growing, more efficient economy.

Bush certainly can make a real case on those grounds, but Romney did, too.