I can foresee such a plan backfiring. Sure, perhaps destroying enough jobs would create unrest directed at the government. Perhaps instead it would create disgust towards the private sector. The thing about a left-leaning government is that it is at its strongest when people struggle. Who cares about public healthcare if they can easily afford their own insurance? Why give a damn about unemployment services if your job seems safe and your boss isn't laying people off? Who is more likely to want an abortion, the one with a constant income or the one with concerns over their future? Who is going to fret more about taxes: the gainfully employed, or the people with no income to speak of?
Therefore the very worst thing a Republican can do is sabotage the free market's ability to generate prosperity. That just makes the public sector seem heroic. Additionally, increasing unemployment means that the Government – always an equal-opportunity employer – gets to hire workers on the cheap, allowing them to complete more works that would garner favour during the next election. Reducing productivity hurts the entire nation and everyone in it, but politically it hurts the Right Wing most of all.
Those bosses who are laying off in response to the elections are going to see one of two things: either there are not enough of them to have a meaningful effect and they just lose business, or they are enough of them to influence politics and they discover that both the employees they laid off and the employees they didn't are now voting Democrat. The Republican party should be calling these clowns and yelling "STOP HELPING ME, YOU'LL RUIN EVERYTHING!"