The Washington Post's poll measured how support for certain policies increased or decreased when then President's name was associated with those policies. For example, Democrats were more likely to support "Obama's Assault Weapons Ban" than "An Assault Weapons Ban" and Republicans were more likely to oppose "the Obama Administrations' attempts to address climate change" than "attempts to address climate change."
But the real gem in this data is the way that Republicans react to immigration reform when Obama is associated with it as opposed to the way that every other group reacts. To be fair, Democrats, Republicans, and Independents are more in favor of a path to citizenship for illegal immigrants if President Obama avoids the issue than if he injects himself into it, but Republican support for such a policy takes a staggering 21 point hit when it is associated with President Obama (as opposed to a much more modest 3 or 9 point hit for Democrats and Independents respectively).
Moreover, that 21 point hit is enough to push Republican support below the 50% mark, meaning that the Republicans would likely not support a path to citizenship if Obama spearheads it.
For Democrats, this is a gift. By making immigration reform a major policy goal of the Obama administration, Democrats can secure their position with the Latino community (which is demographically good politics) while at the same time either forcing the GOP to oppose the measure or commit political seppuku by splintering into centrist and far-right elements.