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Unfortunately the cops were correct. A breathalyzer is a test that is very timely and has to be done within a certain time frame. In almost every state in the Union, you have no right to have a lawyer present when you take a breathalyzer. You can ask for a lawyer, but it can count as a refusal. In most states, a refusal means an automatic suspension of your drivers license.
After a breathalyzer if the refuse to let you speak with a lawyer, then they are denying your right to counsel and anything you said after that time could be suppressed.
I hope this has been helpful. If you need further information, please let me know.
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