President Obama recently said he would issue an executive order to stop the deportation of undocumented immigrants with family members in this country. And the Republicans went ballistic -- claiming the president didn't have the right or power to issue that order (even though they were perfectly happy with the executive orders issued by Republican presidents in the past, including those providing amnesty for immigrants). In short, they seem to be taking the position that executive orders are only permissible if they agree with them (or they're done by a GOP president).
This brings up the question -- what does the general public think about executive orders? The top two charts answer that question. A clear majority of Americans don't have a problem with a president using executive orders (including a clear majority of Republicans). But as the second chart shows, that has some exceptions. Note that only small minorities were willing to go on record as saying those orders were either constitutional or unconstitutional, while bigger percentages said the constitutionality of those orders depends. If they agree with an order, then it is constitutional (and permissible), and if they don't, then it is unconstitutional (and not to be permitted).
So, what does the public think about President Obama's immigration order? They are split, with neither those supporting or those opposing getting majority support. Some groups support the order (Democrats, young people, Blacks, Hispanics) and some are opposed (Republicans, Whites, men, those over 45), while other groups are split (women, those between 30 and 44). Because of this split, I doubt we'll see anything more done on immigration (other than some whining from congressional Republicans) -- either by Congress or the president.
I was pleasantly surprised to know that in all groups but one, people knew that at this point in his presidency, George W. Bush had issued more executive orders than President Obama. Only the Republicans were willing to deny history (and claim Obama had issued more).
These charts were made from information in a recent YouGov Poll -- done between November 22nd and 24th of a random national sample of 1,000 adults, with a margin of error of about 4 points.