Texas has done some of both. There are a set of checkpoints that are permanent enough that they appear on the official state highway maps. The roads and population get pretty sparse, so a more limited number of control points will cover the paved roads if they are away from the border. Some of this area coincides with Eagle Ford Shale zone - where fracking has led to an oil boom accompanied with additional unpaved secondary roads and truck traffic.

During this past Christmas/New Years week, I drove to Brownsville, TX and cycled back along the Rio Grande valley to Laredo and then via San Antonio to Austin. That week there was a huge police presence along the border. One motel I stayed at in Zapata TX had 21 state highway patrol cars parked in front. Each of the first two days I counted >8 cars pulled over and stopped - and many more state highway patrol along the road and on cross-roads observing traffic. I watched one incident unfold ahead of me as a car was pulled over on opposite side of the road. After I passed a little way, I turned back to take photographs and saw the highway patrol get accompanied by border patrol vehicle and then second highway patrol.

I asked some of the state patrol I met in towns and they told me "the governor sent us down". Apparently, state of TX decided to do an extended surge of highway patrol to saturate the border. It was not a wise time to be speeding on the roads. Other than passing stopped cars and a pretty visible highway patrol presence, I didn't notice much else and also didn't have encounters with police other than passing them and smiling as eyes met.

Recently, there is a fair amount of attention paid by state legislature and governor of TX on border presence. Whether that is a natural response to terrorism or a bit overblown varies based on political position. However, what I did see is a lot of normal cross-border traffic, trade and area where people might normally more frequently cross for legitimate reasons. Having checkpoints away from that border puts them in an area where most auto/truck traffic gets funneled through a much smaller set of points and also avoids normal back/forth on border crossings themselves.