Seems the answer, according to Gallup, is Not so much.
Recent polling data shows that:
The amount Americans worry about the various [environmental] threats tends to rise and recede in unison, with concern higher in the late 1980s and early 1990s during the revival of environmentalism, and in the late 1990s and early 2000s amid the economic boom. Since then, Americans' worry has fallen, with concern dipping to record lows on most issues in 2010 or 2011. The current level of worry on each issue remains at or near those record lows
And what they do worry about tends to be those threats of an immediate nature as:
Americans express the greatest worry about pollution of drinking water …
… the least about global warming or climate change.