I do like the idea, but a cursory look at their 'receipt' and where the numbers come from showed a pretty large flaw: half of social security and medicare is paid for by employers. Unless you consider your salary to be an extra 8.65% than it really is, you're not accounting for all the taxes the government receives based on your paycheck. Although this is really a "hidden tax" on your paycheck, most people don't think of it as part of their salary (which is why they do it this way).
There's also other types of taxes paid by non-individuals, like corporate taxes, estate taxes, and the like.
In any case, it means the numbers in their receipt for SS and Medicare are off by a factor of 2, so you should evaluate this only based on the idea, not on their actual numbers. (Not to mention there are likely an abundance of other problems with this method, like spending that is not part of the budget, or when the government is over-budget and issues bonds to pay for it.)