That's a might tall task, considering the many, many different facets and influences of the current tax code. But I'll give it a try.
The absolute worst thing about the NRST is that it is a gigantic, oversimplified, one-size-fits-all panacea. All forms of taxation, be it sales tax, income tax, inheritance tax, payroll tax, tariffs, property tax, excise taxes, etc. etc. have their own characteristic influences on our economy. Given the size and complexity of the federal government, providing its massive funding requirements through a single, oversimplified revenue source (a national sales tax) would amplify those economic influences that are inherent to a sales tax severely out of proportion.
The primary criticism of a sales tax is that sales taxes are inherently regressive. That's to say, people on the lower rungs of the socio-economic ladder bear the brunt of the tax burden because they must pay a larger percentage of their scant resources to pay taxes on the necessities of life: food, clothing, shelter and medicines. NRST proposes to lessen this effect through Social Security "rebates", but that's just another variation on the same old socialist income redistribution scheme of one group of taxpayers subsidizing another. (Even worse since it abolishes the pretense that Social Security distribution is based at least in part on previous contributions.) For the most part, the rebate subsidy will be paid by the Middle Class to those lower down the ladder, undermining the Middle Class. More affluent people will be far less affected as a percentage of their resources. And payment of "universal rebates" to everybody only raises the question of why the sales tax rate was set so high that rebates to everyone is even necessary.
Another inherent effect of a sales tax is that it discourages consumption of the item being taxed. So a 23~30% federal sales tax (depending on how you calculate it) would inherently stifle consumption in our "consumer oriented economy". At such high tax levels, one could also expect that the predominant form of tax evasion that would emerge would be the classic "Black Market".
Another inherent effect of an "all-the-eggs-in-one-basket" nature of the NRST proposal is the way federal revenues would fluctuate with economic business cycles. In times of economic prosperity, federal sales tax revenues would balloon, tempting the bureacracy to squander the surplus just like we've seen many states do during the boom of the '90s. But when economic downturns inevitably occur, sales taxes fall off precipitously, just like we're witnessing in California. All in all, a pretty unstable situatation that wouldn't be tolerated by Congress. So in the end, no matter the ideal vision of "reform" espoused by NRST advocates, you know as well as I do that the Congresscritters will set about to distort the NRST just as bad as the Income Tax before the ink is even dry.
Is this my "best arguement" against the NRST? No, IMHO it's more effective to address specific parts of the proposal as I frequently do. But this does provide somewhat of a summary. I'm not entirely opposed to the concept of a national sales tax. Perhaps a lower sales tax of 5% on non-necessities could be implemented to lower other forms of taxation. But this all-in-one panacea to scrap all other taxes is simply too extreme and outlandish. The government (and we the taxpayers) are better off spreading the tax burden and effects of taxation over the economic stability of multiple types of taxes.