The Washington Post's Chris Cillizza does a nice job of debunking the notion that President Obama faces a problem with his base:
In Gallup's latest weekly tracking polling, Obama's job approval rating stands at 43 percent among the general public but is nearly double that - 84 percent -among African Americans. In the November NBC-WSJ poll, Obama's approval rating among black voters stood at a stratospheric 91 percent. […]
Although African Americans remain the base group most broadly supportive of Obama, liberals and Democrats are very much in his camp as well. In Gallup's most recent data, Obama's job approval rating stood at 78 percent among Democrats and 70 percent among liberals.
The important thing to remember in any discussion of Obama's base - and the Democratic base writ large - is that African Americans loom large. Absent 85-percent-plus of the black vote in national elections, Democrats would have an incredibly hard time of winning the presidency.
It should be said that the flip-side to Obama's non-problem with his base is the fact that he doesn't have a particular problem with any given demographic group, outside of the usual difficulties that come with being a Democratic politician. If Obama is lagging with Latino voters – something Cillizza points out – it's because he's less popular with voters overall, of whom Latino voters are a large subset. In other words, if Obama wants to improve his position with particular groups, he should work to improve his position with everyone, i.e., improve the economy.