It wouldn't constitute patient abandonment if you signed your patients out to someone else when you left. Nor would it if you came late- you can't abandon an assignment you haven't yet accepted. This, of course, does not necessarily mean that your employer wouldn't try to punish you for coming to work late... even if it was to vote.
Every state has different laws as far as time off to vote goes. In my state, the law is:
"Time Off to Vote
Massachusetts laws requires that employees who apply be granted a leave of absence to vote during the two hours after the polls open in their districts. Payment for voting time is at the discretion of the employer. Most employees have time to vote before or after work. One or two hours in most cases is the maximum time needed to vote. Employees should explain their reasons for needing more time and may also be requested to prove that they have voted by providing the name of the precinct where they cast their ballot."
Polls in my state are typically open from 7am-8pm. Depending on where one lives, one may reasonably be able to vote exactly at 7am and then make it into work without too much delay. And, depending on where one lives, one reasonably may not be able to do so. My former hospital had a policy that "employees should make all efforts to vote on their own time." Basically, they expected that if you were scheduled to work on election day and you wanted to vote, you would go out of your way to get an absentee ballot. I missed voting in the Special Senate Election in 2010 (the only election I've missed voting in since I was 18) because I had to work a 12 hr shift and my work would not allow me to leave for a short period of time to vote. My voting place was 3 miles from the hospital. I probably should have applied for an absentee ballot but, if I remember correctly, I didn't know I was working that day until shortly before the election because our schedule didn't come out in any reasonable amount of time. Fortunately, this year, it's not an issue because I work 7:30-3:30 on Tuesdays.