Can the police charge me with a breathalyzer refusal even though I tried to blow into it?

Yes, you can be charged with a refusal even though you tried to blow into the breath test machine. However, you may have an absolute defense to that. Such as, you may have been suffering from a medical condition, or you may have been just physically incapable of blowing into that breath test. Keep in mind though, that ultimately it's up to the judge or jury to decide as to whether or not that refusal to submit to that breath test was willful.