Their amendments to the budget, with debate ongoing now, give us some clues. Amendment #164, from Sen. Kelly Ayotte, would delay PPACA. Kansas Sen. Pat Roberts has two PPACA delay amendments, one that would hold off on the law if it increases overall health spending, one if it increases federal health spending. Idaho Sen. Mike Crapo would save people in lower income brackets from the mandatory taxes that make the law work. North Carolina Sen. Richard Burr would simply repeal all the taxes. Wyoming Sen. John Barrasso, a doctor, attempts a clever runaround that would also stamp out Obamacare: No mandate "unless PPACA reduces premiums." And then, garnering all the fanfare and hype, is Texas Sen. Ted Cruz's amendment to simply repeal PPACA.
The punchline? The budget resolution is so called because it's a resolution. To defund Obamacare, you're gonna need to do it in the CR (which just got passed with no Obamacare-defunding hoojoo), or do it in another spending bill. These various amendments are letting us know how many Republican voters will be there when the next crisis, the debt limit, brings Republicans another chance to limit spending. But that's pretty much all they let us know.
Correction, March 22, 2013: This post originally misspelled Sen. Mike Crapo's last name.