Likeability lends a president some influence with congress in that he is able to call on their constituents to pressure them on issues. Reagan was the master at doing it.
It's more important for a presidential candidate, however. Getting elected in this era of mass imagery requires a projection of it. Enough voters cast their ballots on the basis of feelings rather than rational thoughts to make it crucial.
Bear in mind that projections are not necessarily real, and so we have to say it's critical for someone running for the presidency to appear likeable, not actually to be so when the cameras aren't running. Just as Reagan was genuinely likeable, Obama is brilliant at projecting a false likeability, or rather one of a number of versions of it depending on his audience at the time. It serves just as well.