Washington (CNN) – With the clock ticking towards two crucial deadlines, a new national poll indicates congressional Republicans would shoulder more blame than President Barack Obama for a possible government shutdown.

But according to a CNN/ORC International survey, support for the president’s health care law appears to be waning.

The poll’s Wednesday release comes less than three weeks before the current measure funding the federal government expires on September 30, setting up another budget battle between congressional Republicans and the White House. That deadline comes one day before a key element in the Affordable Care Act, better known as Obamacare, takes effect. Enrollment in the health care exchanges that form the core of the new law begins on October 1.

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