Point of order here, Grz...if the existing US 59/TX 151/AR 151 freeway in Texarkana is going to be designated as I-369, doesn't that make that proposed Western Bypass obselete?? If that proposed route was to pass, you'd still have a gap on existing US 59 between the point where the bypass breaks off to the existing interchange with TX 151 that would have to be upgraded to Interstate standards...and how would you designate the bypass, then, if I-369 has already been assigned to the existing freeway + upgraded US 59??
Wouldn't it make more sense to run I-369 along the proposed Western Bypass ...
My suspicion is that the current I-369 is an I-69 placeholder, i.e. since it was the only interstate-grade segment between I-30 and Tenaha, Texas officials went for the I-369 designation in order to keep the Tenaha-Texarkana segment "in the game".
* I believe that there is a fear that the nearby, somewhat parallel, I-49 corridor might be viewed as making a "spur" interstate grade upgrade of US 59 unnecessary. Immediate installation of I-369 signage may be an effort to forestall that possibility. Ultimately, I think the local officials would prefer to have I-369 run along a West Loop to the TexAmericas Center, as a recent report suggests:
The I-69 Advisory Committee Report and Recommendations, combining information from the five segment committees (and current to November 5, 2012), has been posted on the TxDOT website. Even though US 59 has received conditional approval for the I-369 designation, the Report contains a map showing an I-69 route through the TexAmericas Center and related comment (page 16/30 of pdf; page 10 of report):

Projects in I-69 communities show how this Interstate is important to freight movement, economic growth and job creation. Examples include the TexAmericas Center, planned to be one of the largest rural business and industrial centers in the United States. This center is planned to encompass nearly 13,000 acres along I-30 just west of Texarkana.
Also, the tentative TexAmericas Center West Loop routing provides a feasible connection to a Northern Loop I-49 connection (development has essentially killed that possibility for the current I-369). It is certainly possible that neighborhood opposition may kill the West Loop; if so, they would find a way to upgrade the US 59 corridor from TX 151 southward. If a West Loop alternative is chosen and built, then I don't think the current I-369 will ever connect to the rest of the Spur. I think they would decommission the current I-369 and reassign the designation to the West Loop. The current I-369 would either revert to US 59 or receive another I-x69 designation.
edit * Since I-369 is already connected to I-30, TxDOT did not have to make a representation to FHWA that it would be connected to the interstate system within 25 years.