There are scads of chain motels along US 83 in the Lower Rio Grande Valley, so finding a place to stay shouldn't be a problem. The Alamo Inn, near Santa Ana NWR, caters to birders and is just minutes away from the refuge.
Hopefully, the birds that have attracted so many birders to the Valley will still be around during your late March trip. Good luck. Please contact me if you have any other questions. I live in Houston and can give you information about that area as well.
Steve in Houston