I'm a foreigner so take this for what it's worth but my view is that if it provides significant public benefit (in reducing drink driving / dope driving accidents) that stops for the specific purpose of breath testing at DUI checkpoints then it should be something the community would support.
How that plays out is another matter.
I lean the other way, and this being one of my favorite quotes probably makes me decidedly American:
"Those who would give up essential Liberty, to purchase a little temporary Safety, deserve neither Liberty nor Safety." - Ben Franklin
That said, I do entirely disagree with drunk driving and I want it to end. I'm just not willing to further trade my personal freedoms to accomplish it.
The supreme court actually decided that it's not unconstitutional but leaves it to the states to handle enforcement.
Interesting to note that in Australia the percentage of fatal accidents involving alcohol are 12% versus 22% in California. Especially because we have a younger official drinking age of 18 and a generally higher alcohol consumption rate...