The president also has a profound impact on independents' support for certain policy proposals. Tying the president to a pathway for citizenship for illegal immigrants actually drops support by nine percentage points. But the president's name gives a renewed assault-weapons ban a seven point boost, increases willingness to address climate change by four points, and spikes willingness to end the Afghan war by 15 points.

The survey results underscore some of the difficulties Obama will face heading into his State of the Union address Tuesday night. He is expected to address each of the aforementioned issues at some point in his speech, highlighting his immigration-reform plan, gun control, plan to pull troops from Afghanistan, and new climate change executive actions. There's advantage in doing so, capitalizing on policies that now enjoy broad appeal across party lines and rallying supporters to advocate for their passage. But the president also risks polarizing an issue, splitting off Republicans who might otherwise support a proposal because they do not like him personally.