Actually, I agree with you. But, this is a case where the GOP might win the battle, but would lose the war.
The Misleadia will demagogue the Republicans for increasing taxes on the poor and middle class, while fighting to preserve the "Bush tax cuts for the rich" (never mind that the poor got a tax cut then, too -- reducing their federal tax bill for some of them to less than zero).
I thought I read that Santorum has suggested that the payroll tax be restored, but give wage earners the option to contribute that extra 2% to a 401(k) instead of Social Security (reducing the wage base used to calculate benefits). I think that's a great idea, but the Democrats would never allow it.
Congress could fairly easily let the Social Security cut expire and implement an income tax credit in the same amount. Of course, it's academic since the Social Security Trust Fund has all been spent anyway.