By Elise Viebeck - 07/19/12 12:15 PM EDT
The current House GOP has held more than 30 votes to undermine the Affordable Care Act, which the Supreme Court largely upheld on June 28.
Republicans most recently led the chamber in a second vote to repeal the law in full. The measure passed 244-185 but will go nowhere in the Democrat-controlled Senate, like most of the others.
Democrats responded by seeking to portray the GOP as myopically focused on healthcare at the expense of other national problems.
Recent polls show this view might be gaining traction with key voters.
According to a new survey from NPR, 51 percent of likely voters want Congress to move on.
The result exactly matched one from the Kaiser Family Foundation, which found on July 2 that 51 percent of independent voters want opponents of the law to "stop their efforts to block" it.
Opinion of the law remains divided overall, with roughly half of Americans expressing support and the other half opposition.