No, not the presidential primary. That will stay in March, unaffected by this proposed legislation.
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Massachusetts has tended to have a later than typical statewide primary compared to most of the rest of the country, sandwiching a general election campaign into a seven week window between an early September primary and a November election.
However, recently proposed legislation would reconfigure that set up. S 391, introduced last week by Senator Jason M. Lewis (D-Fifth Middlesex), would shift the statewide primary from the seventh Tuesday before the general election (which tends to fall in early September) to the third Tuesday in May. The practical effect, if this bill were to be passed and become law, is to tack an additional ten or so weeks onto the normal general election campaign for those running for federal/congressional and statewide offices.
And, in fact, that is part of the cited rationale behind the legislation: to mimic other states with earlier primaries as a means of increasing public engagement and, by extension, turnout. The move would also eliminate the late summer and early fall calendar conflicts that can arise. The scheduled primary's overlap with Labor Day in both 2012 and 2016 forced those primaries from the Tuesday immediately following the holiday to the Thursday of the same week. The former also conflicted with the Democratic National Convention.
This is not a new idea in the Bay state. For the last several years there has also been legislation to consolidate the Massachusetts primaries -- including the presidential primaries -- in June. Those efforts have met dead ends in the past. Whether this new bill meets the same fate remains unanswered.