Meh, I don't see it.
The Brexit vote isn't the key piece now. It's the fallout.
If it's a disaster for Great Britain, then anyone who supported it will be tarred by it.
And it's looking like we might be seeing the death of the United Kingdom in our lifetime. Replaced with a unified Ireland and an independent Scotland. The motions are already being started to hold another Scottish independence referendum. And the Northern Ireland government has already stated that the Brexit vote didn't represent them.
Being that Ireland is already in the EU, we could easily see a vote to leave Britain and join Ireland that would be supported by the Catholics that already want that... and the Protestants that don't want to see a collapsing economy. (providing that happens, though)
Not to mention how the EU (namely France and Germany) are now pressing for an immediate break with the UK, ending the treaties and agreements ASAP... the shock of that alone will drastically hurt London and the UK financial sector. Which plans a massive part in the UK economy. If that goes, then the UK *IS* in a recession, if not a depression.
And to anyone saying that this will take a long time to play out... we have months yet to go before the election.
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All that will be used to tar those politicians in the US that supported it. Which casts doubt of the judgement abilities of those politicians in the minds of the electorate.