The idea behind this is two-fold -- to supply the states with a sales tax some extra revenue, and to level the playing field for local businesses (which have to collect the tax). The first reason may be its death knell, since few representatives are going to want to be seen as supporting any kind of new tax (especially since it won't help solve the federal deficit). And the second reason probably misunderstands why people buy on the internet. It is usually done because it is so easy and the itms are delivered to the buyers door -- not because a few dollars can be saved on a sales tax.
So what does the American public think about taxing internet sales? Most are against it. The Gallup Poll did a survey on this question on June 15th and 16th. They surveyed 1,015 nationwide adults, and their poll has a margin of error of 4 points. As you can see from the chart above, about 57% of Americans oppose the internet sales tax, and only 39% support it.
One interesting aspect of the survey is that younger people don't like it by large percentages (the 18 to 29 and the 30 to 49 age groups). It is only older Americans (50 and over) that are split on supporting and opposing the tax (with the results being within the margin of error, and therefore not a statistically significant win for either side). The chart below gives a demographic breakdown on how different groups see the issue: