Last week, YouGov/Polimetrix asked a sample of 1,000 adults about a flat rate income tax. We commissioned the poll to survey Americans on their opinion of changing from our current income tax system to a flat tax system under which all but low-income Americans would pay 19% of their income in taxes, regardless of how much money they make.

Flat tax proponents face an uphill battle. Americans in general opposed the flat tax proposal 39% to 28%. Democrats opposed the flat tax by a wide margin, 52% to 19%. More Republicans supported the flat tax proposal than opposed it, but even then, a majority did not favor it (45% in favor to 33% opposed). The level of support is only slightly higher among registered voters who say they will vote in a Republican primary or caucus next year. These Republicans favored the flat tax 48% to 30%.

But fully one-third of all respondents in our survey were unsure about their opinion of the proposed flat tax. This high degree of uncertainty is consistent with a recent Rasmussen poll of likely voters that asked about a 17% flat tax on income over $17,000. In the Rasmussen poll, 42% opposed the flat tax, 31% favored it, and 27% remained undecided.

Surveys conducted in the late 1970s and early 1980s found similar high rates of uncertainty in public opinion about the flat tax. During this earlier period, one-fifth to one-quarter of Americans reported that they were not sure about their position on flat tax proposals.

In the late 1990s, there was a sustained national debate over the flat tax, spearheaded by Republican presidential candidate Steve Forbes and House Majority Leader Dick Armey. What did Americans think about the flat tax then? Using the Roper iPoll database—a curated repository of public opinion surveys conducted by reputable polling organizations, including the NBC/Wall Street Journal poll—we identified 10 surveys from 1995-1996 and two from 1999 that asked respondents to choose between a graduated rate income tax system and a flat, single rate income tax.

Support for the switch to a flat rate system ranged from a low of 38% in late 1995 to highs of 48% and 49% throughout 1996. In 1999, two surveys that asked Americans to make the choice between a tax system under which higher earners pay higher rates and a single rate for all taxpayers reported that 48% and 50%, respectively, supported a single rate.

Today our survey data suggest that the decisive group of Americans who would be needed to create majority support for a flat rate could be those who continue to suffer in our struggling economy.

In addition to the partisan divisions on the flat tax, one of the largest divides in opinion in our survey fell between Americans who have fared better and worse in our difficult economy. We asked respondents about the change in their personal finances over the past year. Among the roughly half (or 48%) who reported that they were better off or about the same financially now as one year ago, 46% opposed the proposed flat tax, 29% favored the flat tax and 25% were unsure.

Contrast that group to the 45% of respondents who said their personal finances were worse off. These Americans were about as likely to support the flat tax (31%), but much less likely to oppose it (35% opposed) and much more likely to be unsure about their position (34%). That's a big percentage of undecideds up for grabs.

Persistent high unemployment, slow economic growth, and calls to "tax the rich" might sway these Americans to stick with the current graduated rate system and possibly support increases in the marginal rates paid by the highest earners. So the challenge for proponents of a flat or flatter tax system is to persuade these Americans that a radically reformed tax code would spur the so-far-elusive investment, robust economic growth, and job creation that would make them better off a year from now than they are today.

Mr. Brady is deputy director of the Hoover Institution and a professor of business at Stanford University. Ms. Frisby is a research fellow at the Hoover Institution.

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