No, they can't legally demand you open your trunk or search your car at an INTERNAL roadblock away from the border. Note that they can ASK you to open the trunk or search your car, but you are within your legal right to decline. If they ask, then that is an indication that they can't legally do it without cause.
Please take a look at the two Youtube videos I have attached. One is a totally hilarious video of the motorists turning the tables on the checkpoint guards.
The other video is Terry Bressi of Checkpoint USA. Terry settled his border patrol case several years ago for $210,000. The Border Patrol and the local Indian Tribe stopped Terry a number of years back, abusing their authority. I am personally familiar with this case, have talked with Terry by phone, and have corresponded with him for several years. His website is www.CheckpointUSA.org. It will give you a lot of insight.
The suggestions people are providing here are incorrect. The Border Patrol INSIDE the border can't search your vehicle without your consent or without cause. They can ASK, but you can decline. They often ask, knowing that people will not say no because they don't know their rights.
The Border Patrol does not have the same authority INSIDE the border as they do ON the border. Their authority is also different from local law enforcement, which is why they would sometimes call the county sheriff when Terry declined to comply with them. The Tohono O'odham Indian Nation also has a different authority, which was one of the main issues in Terry's case.