I was stopped and the officer told me to take a breath test because I had a beer earlier in the day. I passed, but could I have demanded a blood test instead?
Some states give you your choice and some do not. In a DUI case the type of test you take sometimes is critical. In your case it would not have mattered. Suppose instead, you had a lot to drink earlier in the day, but none for hours since, and you are now back down to a legal blood alcohol level. If you have not urinated since the earlier time, your urine will be of a much higher alcohol level than your breath or blood and will not currently accurately reflect your blood alcohol level. This is why the urine test has fallen into disfavor with law enforcement and is not used in most states anymore.
The question however, is why would you have wanted a blood test? To be sure that any medications or drugs in your system were not overlooked? A breath test cannot detect drugs.