I think the employee portion of the payroll taxes (and personal income tax) being eliminated will result in increased net wages, rather than decreased prices. However, the employer portion will result in decreased costs. Market pressure will determine if the decreased costs result in decreased prices rather than increased profits.
Regardless, to whatever extent the elimination of the existing taxes does NOT allow for reduction of prices by virtue of it being incedent on wages rather than costs, it INCREASE WAGES. Whether it INCREASES WAGES or DECREASES COSTS, it's going to do either one or the other. The only potential for decreasing purchasing power by the wage earner is to what degree the decrease in costs are turned into profit rather than reduced prices, which will still increase SOMEBODY'S buying power.
The net effect is that (if it is revenue neutral), then, overall, purchasing power on average should be the same. There would be some consumers who would be expected to have increased purchasing power, and some to lose some, but over all, it should net out.
However the fact that resident aliens (legal and illegal) and others not currently paying income tax will now pay sales tax should broaden the tax base. This will put those people in the position of having less purchasing power, and have a net benefit to the purchasing power of those who pay taxes, now.
It will almost have to reduce the price. Adding a 30% sales tax on goods, while perhaps decreasing costs 10% will put heavy pressure on prices. I can't imagine this plan being good for people on fixed incomes who will not have the added purchasing power from the eliminate Payroll Taxes, but will have to be faced with paying more for goods and services.