What Republicans are doing is conducting guerilla attacks. That is, they are focusing on small parts of the Affordable Care Act and trying to repeal them one by one.
For example, the House of Representatives has overwhelmingly voted to repeal the tax on medical devices. The House has also passed a measure that would repeal an independent review board that is supposed to keep Medicare spending in check. The House has a lawsuit under way that challenges the administrations right to reimburse insurers for cost-sharing subsides for low-income families and the administrations decision to change the timeline on the introduction of the employer mandates.
But what is the point of all that? Even if the Republicans are successful on all fronts, at the end of the day they are just nibbling around the edges of the Affordable Care Act. For better or for worse, Obamacare will continue shaping our healthcare system unless the GOP offers a clear alternative.