I don't agree with that reasoning. It feels that we just look at the numbers, and punch them in. There were many people that were surprised that they had to pay extra taxes this year.
That said, my sense is that most people don't know what their total yearly tax is, nor their tax rate is, only their refund/tax payment that's due in April 15. As the Republicans found out recently, a lot of people complain about their "tax increase" when they don't don't get a refund, even if their actual tax rate went down.
* Special interest groups who have won tax credits/deductions--most of these don't get reported to the IRS, so it makes it easier to kill these off since fewer people will take advantage of them.
* The anti-government crowd, who is a) afraid that the IRS could abuse this power to tax people more (if people get used to signing the dotted line, they might not notice if the IRS stops accounting correctly for some reason); b) adamant that people know just how much the government is "stealing" from them in taxes and so form a ready constituent for lower taxes; and c) generally don't like the idea of the government telling them what to do anyways, so the government just sending them a bill is the ultimate anathema.
* People who are underreporting certain classes of incomes who might be afraid that there will be a push for broader mandatory reporting to help make taxes even simpler.
Given that the political power of the second class I've mentioned is quite vast, they are sufficient to prevent the sensible implementation of the IRS-sends-you-a-bill even if TurboTax and the like were to stop lobbying the government.
I mean even in general it's hardly an uncommon strategy by shadier companies to get people to pay more: make the process so convoluted and tiresome that people will pay whatever just to make it all go away (hell, see most of the medical industry for a big current events example). It seems like even if someone did want to embark upon an anti-tax strategy it'd make way more sense to increase transparency and ease, just have a big number in an envelope of "We calculate you must pay $X this year, which is $Y (more|less) then last year". Then if it's significantly more people can just focus on that while fresh, rather then arriving to that result after hours of going through stuff with nebulous "you may be audited by the IRS you potential criminal!" hanging over it all and thus being exhausted.
So even taking Norquist's goal as a given (which I don't) the strategy seems pretty damn stupid to me at least. The primary result has been that I now hate Norquist and every single person who goes along with him, and would cheerfully support higher, easier taxes not just because easy would be nice but also to piss him off.