So, I would think it would come to between 20 and 23 percent of GDP
Okay, I read your post and there's not much detail about where the 20-23% comes from, but you seem to have it in your head as a reasonable guess, and your outline for a rough estimate seems good, so let's accept that for the sake of argument. That would be 0.2 X 14 triillion = 2.8 trillion. Current spending is just over 3 trillion, so that's not too bad, especially if we're going to trim spending in the next congress.
But I still think a few more adjustments are in order. I like the idea of a flat tax on income, but I really don't like the idea of a national sales tax for two reasons. First, as has been pointed out the percent of a family's budget used to consume goes way up as income goes down, so people who can least afford to pay the sales tax are hit hardest. That affects all of us since we end up adjusting the welfare/medicare rolls to even that out. Second, as Michelle Bachmann and others have suggested, it institutes a new tax, and if the past is any guide to the future, then we can expect that tax to increase over time. Eventually you can imagine paying a 20% sales tax in addition to income taxes.
If we lose the national sales tax, and decrease the corporate tax in order to encourage job creation, and increase the national flat income tax proportionately to make it up, I'd be on board. Maybe something like
income: flat 18% for everyone
corporate: flat 5%
sales: none
That would still generate 3 billion or so, and you'd have an easier time selling it to both parties in congress.