Certainly most peoples incomes will go up to make up for the cost increases. The problem is, many sources of income do not have withholdings and will not go up. For example, millions of elderly on Social Security will not see their checks go up. People on tax-free pensions or tax-free investments will also not see any increase in income. These people will be in trouble under the sales tax.
More importantly, this whole thing (admittedly, flat tax would do this too) would destroy an industry that has allowed alot of hard working people to become rich.