Most current Republican positions are actually unpopular (although, alarmingly, the "Terror Babies" amendment to the Constitution is an exception). Repealing universal access to private health insurance is only supported by a third of Americans, which would make a veto a no-brainer. And the GOP third is increasingly white and rural, which means it represents a reactionary throwback, not a constructive move forward. Greater freedom for people to invest their social security in private markets is pretty popular (I support it) but not among the elderly, who will be core to the midterms for the GOP.
All of this suggests to me that whatever mandate the GOP thinks it will get this fall will be very very tricky. They haven't done the hard world to revive their policy agenda, and are riding on some ugly identity politics and recession anger to get back to power. Obama is still remarkably popular in the country given the conditions (doing much better than Reagan was at this point) and his leverage may well be quite acute if the Republicans actually have to exercize responsibility. The Boehner-McConnell divide could widen; and the tea-party/establishment strains intensify.
It's deeply depressing to see the ahistorical and ideological FNC/RNC propaganda doing so well in the country. But it is no cure; it solves none of the deeper problems; it's unserious on the debt; and deeply, deeply dangerous and uber-neocon in foreign policy. You have to have faith that at some point more Americans will acknowledge this and give the president the break he deserves.