According to this article, the Republican Party may hold its 2016 presidential convention in late June. As the article says, that would be the earliest major party presidential convention since 1948, when Republicans met June 21-25 in Philadelphia.
Such an early date would eliminate meaningful presidential primaries in California, Montana, New Jersey, New Mexico, South Dakota, and Utah, the states with June presidential primaries. Republican rules require states to have chosen their delegates 35 days before the convention opens. It is possible the Republican Party can persuade those states to move their presidential primaries to an earlier date. Much will depend on whether the Democratic Party also moves its national convention to an earlier date. In 2012, both major parties nominated in September. Thanks to PoliticalWire for the link.