The bill would be effective as of September 2013, and would thusly impact the midterm primaries next year as well. However, let's examine this bill with 2016 in mind. In presidential election years -- years in which that March primary is of some utility to the state of Texas in the presidential nomination process1 -- this move would have some interesting implications. Basically, the first Saturday in March will precede the first Tuesday in March date both national parties have pinpointed as the earliest date on which states can hold delegate selection events without penalty. In other years, though, the first Saturday in March will succeed the first Tuesday in March.
If this bill had been law in 2012 (and assuming there was no redistricting kerfuffle in Texas), the Texas primary would have been held on Saturday, March 3. That would have been the same day as the Washington state caucuses and three days before Super Tuesday on the 2012 calendar. That would have placed the Texas primary on a date non-compliant with both national parties' delegate selection rules, but would potentially have drawn a lot of attention (and possibly have changed how the campaigns approached not only Super Tuesday but the contests the previous Tuesday in Michigan and Arizona as well).
In 2016, the opposite would be true. The first Tuesday in March happens to be March 1. The first Saturday of the month, then, is obviously after that point. Assuming the nominations are not decided on the likely 2016 Super Tuesday (first Tuesday in March -- though that could be a debatable title for that date by 2016), Texas would still have an advantageous niche carved out on the calendar. In both 2008 and 2012, the Saturday following Super Tuesday [It was in February in 2008.] was a landing spot for a number of small state caucuses. In fact, in 2012, the Saturday after Super Tuesday was the date of the caucuses in Kansas and several of the US territories. Needless to say, if Texas ends up on a Saturday in 2016, it would garner all or most of the candidates' attention regardless of what other states share the date.
This bill differs from the Texas Senate bill that has been introduced to move the primary into February in terms of where the primary would be rescheduled, but the theoretical motivations for the moves are slightly different. The senate bill would move the primary to a point that would threaten the positions the national parties have created for the four carve-out states. The house bill is not nearly so provocative. Both bills, however, would shuffle the Texas primary around in a way that would draw the Lone Star state more attention from the candidates. As of this time, neither bill has any institutional support (co-authors or co-sponsors) outside the primary authors of the bills. It is, then, a little early to project how successful either will be in navigating the legislative process.
1 Earlier has proven to be "better" more often than not in the post-reform era in terms of when presidential primaries are scheduled. In contrast, there is no similar race to the front among states for midterm election influence. The byproduct of an earlier primary is a longer general election campaign. To be fair, that is a potential drawback to a frontloaded presidential primary process as well, but there are multiple contests determining any presidential nomination. Without a runoff, most midterm primaries are one-off deals that immediately feed into the general election campaign.
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