A flat tax like the one proposed today by Republican presidential candidate Gov. Rick Perry engenders a split decision in public opinion — if not the warmest reception, a better one than the public’s broader disapproval of his rival Herman Cain’s 9-9-9 plan.

While a flat tax divides the nation overall, moreover, it resonates most strongly in a group of particular interest to Perry – “very conservative” Americans, a key GOP voting group. They hold favorable views of a flat tax by a broad 68-28 percent in this ABC News/Washington Post poll, suggesting a strategic rationale for Perry’s initiative.

More broadly, there’s greater division: Americans overall split by 47-48 percent on the notion of a flat tax – that is, removing most income tax deductions and charging all taxpayers the same tax rate, instead of charging higher rates on higher incomes. That’s almost identical to the 48-48 percent split on a flat tax in a different ABC/Post question back in August 1996.

Views are more lopsided on Cain’s idea of setting the federal income tax, business tax and a national sales tax at 9 percent each. Americans by a 20-point margin, 56-36 percent, hold an unfavorable opinion of the 9-9-9 plan. And intensity runs against the idea: it’s seen “strongly” unfavorably rather than strongly favorably by a 3-1 margin, 35 percent vs. 12 percent.

SPLITS – While partisan and ideological divisions mark these views, so do other factors in this poll, produced for ABC News by Langer Research Associates. In both cases, for example, the new tax approaches are significantly more popular among better-off adults, those in $100,000-plus households, vs. those with annual incomes of $50,000 or less.

In the better-off category, 58 percent favor a flat tax system; that drops to 44 percent among people with incomes less than $50,000. And while fewer than half of wealthier adults, 49 percent, like 9-9-9, that falls to 33 percent in the lower-income group.

Politically, favorable views of a flat tax peak at 56 percent among Republicans, but subside to 46 percent among independents and four in 10 Democrats. The 9-9-9 plan, for its part, doesn’t win majority backing in any of these groups. It’s seen unfavorably by 50 percent of Republicans, rising to about six in 10 Democrats and independents alike.

IDEOLOGY – Some of the most striking divisions are ideological, with results shedding light on the positioning of Perry’s flat-tax proposal. He’s done best in support among very conservative Americans, an overwhelmingly Republican group that’s been less supportive of Mitt Romney. But Perry has been challenged lately among strong conservatives by Cain.

The flat tax looks to be Perry’s pushback. As noted, very conservative Americans express a favorable opinion of a flat tax plan by a vast 40-point margin. The same group, by contrast, only divides on 9-9-9, with 46 percent seeing it favorably, 49 percent unfavorably.

As a broader campaign theme, though, a challenge for Perry is in extending flat-tax support beyond very conservatives. Favorable views of the idea drop by 17 percentage points, to 51 percent, among people who call themselves “somewhat” conservative; and fall farther, to about four in 10 favorable, among moderates and liberals alike.

OTHERS – There are differences among other groups. Both plans are about 10 points more popular among men than among women, even after controlling for political and income differences. The 9-9-9 proposal does better with younger adults and less well with seniors; a flat tax skews in the other direction – more popular with older Americans.

And education is an independent factor in views of a flat tax: People who’ve done postgraduate work are much more likely to look askance at the idea, responding unfavorably by nearly 2-1, 62-34 percent. Since education predicts voter turnout, that, too, may be a longer-term challenge for Perry and other flat-tax proponents.