I don't see how. The middle class depends on the economy working (the rich do not, they can leave).
Firstly, that is not a very patriotic opinion. But I will not press that issue right now except to point out that, while this may be true, people would really rather not hear it.
And to answer how, taxation removes money from the economy that could have been invested or could have been used to create supply and also demand (Say's law, or the converse proposed by Keynes). It lowers GDP. However, while targeting the rich in particular will probably reduce supply, or cut production, at the same time, the money taken from the economy can be used by the government to, say, improve school systems or to ensure medical care for our nation's less fortunate. And to top it off, the social ladder is shortened because the super rich are closer in income to the working class.
But another key issue with McCain is that he wants to cut corporate taxes. The idea is that this allows corporations to generate profit more easily and thus produce more. More companies will come, more risky investments will be made, etc. Basically, there would be greater supply and thus greater demand. However, while there is greater supply, it can be argued that workers in these companies would not benefit as much. The CEO's would be making a lot more profit, but wages would be dictated by the amount workers are willing to work for. Unemployment might drop even, but ultimately, workers lose buying power compared to the rich (I am not entirely sure about this, but it is an argument that has been proposed to me.). Altough, an interesting idea is that their buying power might exceed what it would be if the economy were weaker. Who knows? It really boils down to people rather having a poorer country in which people are closer together economically over a country that is very rich but that exploits its workers.
[I really ran past my knowledge with this one. Feel free to prove deductively how something I said is wrong. I would be interested in seeing how.]