I know Texas has an extension of time to file franchise tax reports. Does it also allow an extension for sales & use tax reports?

Yes, but prior to the due date, you must pay 90 percent of the estimated tax due and provide a written request for extension that indicates good cause.

The extension period is 45 days (90 days if you are the victim of a natural disaster). It seems that hurricanes, tornados, and such are fairly common in the Republic of Texas.