Romney would direct DHS to grant waivers to all 50 states via executive order. Although someone from Heritage testified the waivers are unconstitutional, Nevada did get one.
Perry's said he'd sign an order that "eliminates as much of ObamaCare that I can have done with an executive order." It's entirely likely none can be but that doesn't call into question his intent. Under Perry, Texas is a member of the multi-state lawsuit against ObamaCare.
What might be done in terms of halting implementation or waivers all depends on the discretion given by Congress in the bill.
This Newsmax pundit supports Bachmann.
“Bachmann Corrects Opponents on Overturning Obamacare”
http://www.newsmax.com/InsideCover/Bachmann-Perry-Romney-healthcare/2011/09/08/id/410227