The following seems to be reasons given for why checkpoints are allowable: (Please note, not my opinions, but what I've found from looking at past Supreme Court decisions relating to the subject. I know, nerdy, but hours of research is how I got through college -- my professors would rip you a new one if you failed to back up a paper with legiimate research and valid citing sources)
1. A checkpoint involves checking everyone that passes a specific point on a road; no one is singled out at the discretion of an officer. It’s not random with respect to who is checked, as all that pass are checked – even if but very briefly
2. The operation of a vehicle is a privilege, not a right. Your right to use the road is not being disallowed – you still have access – but there are conditions that you must meet to be allowed to operate a vehicle on public roads. Your ability to meet the conditions of that privilege can be assessed.
3. If probable cause is present, then an officer is not violating your fourth amendment rights if he/she assesses your ability to operate a motor vehicle, i.e., if you present signs of being intoxicated, it is not an “unreasonable search and seizure,” which the fourth amendment protects you against.
4. If you refuse a breathalyzer, and there is a judge present at the checkpoint, and probable cause exists, then yes, he can issue, right there and then, a warrant, supported by oath and affirmation, and which describe the “place to be secured, and the persons or things to be seized.”
Now granted, the Supreme Court may someday hear a case before it that prompts them to decide that checkpoints do somehow infringe upon personal freedoms or rights, but so far their rulings have not cast any light of unconstitutionality on the practice. Note however: one key point that has held them to support it is findings that show checkpoints are effective; the findings may prove to be wrong, or the numbers may drop to where the lack of effectiveness is outweighed by the inconveiience to motorists.