It turns out that Republicans don't approve of all tax cuts after all. Those small-dollar increases in after-tax pay don't please them. They assert that they tried it before and it didn't work. Now, what they tried before was a refund which all too many people used to pay down debt or increase savings (normally a good thing but not in this particular downturn). They don't understand that a little extra in each paycheck may be more likely to be spent just because it is so small. Sure, some people will still save it or use it to pay down debt. But if you get just enough extra to buy a latte or a Big Mac, there's a reasonable chance that's what you'll spend it on.
No, Republicans want the usual Republican tax cuts. Two deserve special comment. Cutting the corporate tax rate is not going to create jobs. (Full disclosure here: I am not an economist and barely survived Econ. 101, but that lack of background doesn't stop other people from asserting uninformed opinions so I see no reason why it should stop me.) Companies are shutting plants and laying off employees because nobody is buying. Demand has dried up. These companies aren't going to open up those plants and hire back employees to sell goods nobody is buying just because their corporate income tax rate has dropped.
The other suggestion, the payroll tax holiday, is disastrous on three grounds. First, it is another frontal attack on the funding of the social security system which, of course, Republicans still want to kill. Second, these cuts can mean to many workers a significant (two-three figures) increase in take-home pay. That is sizable enough to risk that much of it will be hoarded (saved or used to pay down debt) rather than spent. Third, it will hurt like hell when it is reinstated.
And that last point is the most important reason for objecting to Republican tax cuts. Those tax cuts, whether for payroll taxes or income taxes or whatever, will have to go up when the crisis is over. And that will give Republicans the club they love to use: liberal Democrats are raising your taxes to pay for all those awful liberal programs. And probably no tax increase would be felt as strongly by ordinary citizens as the reinstatement of payroll taxes after a 6-month or 1-year holiday.