That's exactly right. The Republicans are trying to say that Obama's "redistribution" comments indicate that he's a Marxist/Communist/Martian/Socialist, when in fact there are essentially just two elements at work here: How much people are taxed and where the money is spent. They can spin this all they want, but that's the bottom line.
Much ado about nothing, indeed.
What they really don't want to admit is that any President who allows for funds to go from one place to another is a redistributionist by their standards. Like, say, Reagan. It's just a matter of degree, then.
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You are attempting to rationalize Obama's remarks, by confusing the definition of redistribution to include things it has nothing to do with. The American people have a contract with government. With the federal and state governments, those contracts are the US and state constitutions. With local governments, the contract is codifed in the stipulations that establish those entities.
The people's part of the contract is to pay taxes to fund the government and the services that the contract specifies that government will provide. No different than the rental contract between a lessee and a lessor, or your agreement with the electric company.
Collecting taxes and providing the service in accordance with the contract, is not redistribution in any way, form, or method. Redistribution takes place when government begins giving some of the money they collect in taxes to individuals or groups that have not done anything to earn that money. The billions of dollars that Obama gave to cronies and campaign donors in the form of green energy loans and grants, is redistribution.
Welfare is redistribution.
The earned income tax credit is redistribution. Pell grants are redistribution. The millions given to planned parenthood is redistribution. Foreign aid is redistribution. Our government has found many ways to redistribute wealth, but none of it is in compliance with the contract that government has with the people.
Whether, or not, you are in favor of some or all of this redistribution of wealth, at least recognize what it is, and quit attempting to rationalize it into something it is not.