Seven in 10 people in the survey said they would support a path to citizenship, including 60 percent of Republicans. But when the same question was asked of a separate sample of respondents, this time with Obama’s name attached to it, support dropped to 59 percent overall and just 39 percent among Republicans.

On other hot-button issues like banning the sale of semi-automatic assault weapons or ending the war in Afghanistan, however, lending Obama’s name to the proposal made each viewed more favorably — and therefore if he were to put his political weight behind them it could actually increase their chances of passing. On doing something about climate change, there was no noticeable movement.