And who is it Republicans would like to raise taxes upon? According to the Tax Policy Center, 46 percent of U.S. households won't pay income taxes this year. The elderly (who are mostly retired, have a larger deduction, and often don't have their Social Security benefits taxed) make up a plurality of 44 percent of the nonpayers, while people whose income tax liability is wiped out by the child tax credit, child and dependent care tax credit, and the earned income tax credit—all of which were enacted with Republican support—make up an additional 30 percent of the group. (The rest of the nonpayers get a handful of smaller tax credits, including education credits, itemized deductions, and even capital gains benefits.)
Keep in mind that these people not having any income tax liability does not mean that they don't pay taxes (as is often implied in GOP talking points). They pay state and local taxes, not to mention federal payroll taxes, which of course the GOP wants to see rise.
So Republicans worry about the wealthy paying too much in taxes while fretting about freeloading lower classes. They talk a big deficit game but are more concerned about cutting government spending, specifically on programs that benefit the nonrich. Perhaps this isn't cognitive dissonance but the logical evolution of the modern GOP into an Ayn Rand-ian coalition explicitly focused on freeing a wealthy elite from the parasitical depredations of everyone else.