One solution that a number of people have been working on is called the "Fair Tax." [1]
The general idea (and I'm probably missing some of the significant points, but this is a rough outline) is that there would be no income tax at all — all taxes would be on consumption. Rather than trying to regulate what is taxed and what isn't, everything would be taxed at the same rate.
To fight any regressiveness involved in that, everyone would get a set amount of money every year, which is equal to the consumption tax you'd be paying on the first, say, $30K of purchases a year. So if the consumption tax rate is 25%, you'd be given $7,500 a year. (The term they use is "prebate.") That way, everyone's first $30K of expenses is a wash. After that point, you're only taxed on the money you spend beyond it. The more you buy, the more tax you pay.
A number of Republicans have been in favor of the Fair Tax, and it was one of the planks of Gary Johnson's presidential campaign last year. But it gets support from Democrats as well, and was one of the main components of Mike Gravel's campaign in 2008.
I'm sure others will point out downsides to it, but one that I know of is that current retirees, who have already paid income tax on some of their savings, would have much less purchasing power under the new plan. That is, they'd be double-taxed on the money used to buy goods under a Fair Tax plan. I believe there's also been skepticism from opponents that the numbers actually work out well enough that a Fair Tax system would bring in enough money (as compared with current tax revenues). [Edit: the double-taxation wouldn't be limited to retirees; they're just the group that's often mentioned as being significantly affected.]
(I'm not an apologist for a Fair Tax approach; just wanted to mention it as one theory for introducing a consumption-based tax in the US, in case you're interested / want to learn more.)
1. http://www.fairtax.org/