Would there be an argument that a progressive income tax is unconstitutional based on basic fairness and the constitutional equal protection clause?
Let me address the basic fairness argument first. It seems to me that the basic fairness argument cuts both ways, doesn't it? Is it not fair for those who make more money to shoulder a greater burden for society's needs? On the other hand, is it fair to, effectively, penalize someone for making more money by taxing them at a higher rate? That seems to fly in the fact of capitalism and provide a dis-incentive to earn more, right? That could be debated more all by itself.
The equal protection argument, I presume, would go something like this: It violates equal protection to tax those who make more money at a higher rate than those who make less money? Equal protection analysis requires first that there is a distinct class of people that is being treated differently than another class of people - here, it would be high earners v. low earners, for argument's sake. Then, ask yourself, what is the basis of the differential treatment? Is the basis one that the law regards as suspect? E.g., treating two groups differently because of race is "suspect." When laws differenetiate based on race, they must survive a level of scrutiny known as "strict scrutiny." Under this level of scrutiny, the law almost always fails unless the state can show a compelling reason for the different treatment.
The different treatment in your two groups, or what I presumed your two groups to be, is not suspect - the law does not create classes of earners that are protected. So, a progressive tax law would only have to survive what is called "rational basis" scrutiny. Under this low-level scrutiny, a law does not violate equal protection if the state can show any rational basis for the law - here, the rational basis is that one who makes more money ought to pay more toward society's expenses.
An even more interesting question, though, is whether income taxes are even constitutional at all....