Recently a commission of Republican Party activists submitted their report to the National Chairman, Reince Priebus, on how the party can be more successful in the 2016 presidential elections. Here is a link to the report. The portion of the report that starts on page 69 recommends that fewer primary season debates be held, and the part of the report that starts on page 72 says that the party should hold its national convention in July, instead of late August, and that if the national convention is going to be in July, the party should work to persuade states with June presidential primaries to move them to an earlier month.
States with June presidential primaries are California, Montana, New Jersey, New Mexico, South Dakota, and Utah. Thanks to Frontloading HQ for the link.