The only big cuts Romney ever proposed were to programs that aid the poor. He wanted to block grant -- which is to say, sharply cut -- Medicaid, food stamps, and housing assistance. He wanted to get rid of the tax cuts enacted in the stimulus to help the poor -- that's why his tax plan actually raised taxes on the poorest Americans. He wanted to repeal all the spending in Obamacare, most of which goes to lower-income Americans.
These are, however, classes of cuts the White House won't even consider. A year ago, they were open to modest cuts in Medicaid, but after the Supreme Court's health-care decision, even that door has shut. As for discretionary spending cuts, so many of those were made in 2011, there's just not much left to do.
That leaves Medicare and Social Security. It's possible that the negotiators will enact a backdoor, but significant, cut to Social Security by changing the government's measure of inflation. But they're not going to come at Social Security from the front. It's too politically potent. Even Ryan's budget left Social Security alone.
As for Medicare, as Barro says, if "Republicans ask for near-term Medicare cuts, that will mean reversing a position that is popular with a core constituency (old white people) and giving up a cudgel that they feel they have used effectively to beat up the president since 2009." It's a pickle.