1) lower the income-tax rate on everybody to zero and eliminate the federal government altogether;
2) disenfranchise poor people;
3) raise taxes on poor people.
Not even the Journal wants to shut down the federal government. And it probably doesn't want to take away the vote from people who don't earn enough to pay income tax (though Thomas E. Nugent, on National Review Online, suggests that pollsters stop talking to them). So, the only logical solution is to raise taxes on poor people.
Postscript: Tax-the-poor goes respectable! Robert Samuelson, Newsweek's conservative-but-sensible economics columnist, has written a surprisingly sympathetic column about the tax-the-poor meme. Samuelson raises many good arguments against the meme, among them that rich people are paying more income tax mainly because they're earning more income; that poor people don't vote all that much; and that low- and middle-income Americans don't want to soak the rich because they'd like to be rich someday themselves. (On this last point, Chatterbox should note that the same conservatives who claim class warfare doesn't exist in the United States promote taxing the poor as a means to halt … class warfare.) Samuelson does not, alas, mention state taxes, which are very regressive, and he mentions the regressive payroll tax only in passing. Unlike the Journal, Samuelson suggests that the income tax ought to remain progressive. But he's not sure how progressive it should be and concludes that tax burden should be spread "more evenly." Say it ain't so, Sam!