Yes. It won't happen, though, because most Republicans are too much a part of the DC political class to recognize the need to end ACA. Statists of all sorts view changes like ACA as part of the process. I'm sure there are many Republicans who believe ACA is too complex and costly, but they're willing to work with it to mold it and create efficiency. The idea of taking a bold stance which forces Democrats to take notice of the public's rejection of ACA is repulsive to establishment Republicans.
Ted Cruz, Rand Paul, Mike Lee and a few others who're proposing the defunding understand the destruction which ACA will cause, so they're pushing a defunding of ACA specifically, but Democrats have framed this move as a government shut-down. Democrats are unified around ACA, which is incredible given the public's negative reaction so far.
What we're witnessing is a huge statist change in healthcare that has taken on a life of its own, and the political class has chosen to go along in spite of all the revelations of unintended consequences from ACA. ACA will hurt businesses and, thus, ordinary Americans looking for a good, steady, full time job.
Not only will ACA hurt businesses and job seekers, plus threaten those who presently have full time jobs, it will also hurt healthcare delivery. ACA will cause a brain-drain among physicians. Young people deciding on careers are not likely to choose healthcare if they foresee cuts in pay to make ACA work, and this is what will happen. If you don't think quality makes a difference in healthcare, you'll soon find out how important quality actually is when dealing in professions which require high intelligence. Plus, from all indications, the myriad regulations built into ACA promise to create havoc among healthcare workers which causes stress and unhappiness at work, so even the lower quality workers will be made worse by oppressive, stressful work conditions. It's easy to imagine hospitals becoming nightmares of bureacracy, incompetence and bad attitudes.
Should Republicans, and Democrats for that matter, defund ACA? Yes, yes they should. But only after explaining how a free market approach to healthcare is viable. Despite what was said around 2008, problems with healthcare were not caused by free market principles, but, rather, a lack of free market principles. Something as simple as allowing purchase of insurance across state lines will have a huge impact. The real boost to healthcare through free market principles is innovation and local solutions. ACA doesn't promote innovation and local solutions. Is defunding ACA bold and radical? Sort of, but what's really bold and radical is the demand that government get out of healthcare altogether.