The ideal conservative vision of the tax system is to have lower and flatter taxes, and less social spending. The ideal conservative vision of the economy is one where people keep what they earn, and the amount they earn comes down to their effort, and value of what they produce. You want to improve your position? Just tighten those bootstraps.
But the assumption that conservatives make is that whatever the free market sets for wages and profits for various jobs, people, and businesses, is ideal without any outside influences. And, that any policy affecting the free market is just a negative distortion from that ideal, and is at best, a temporary band-aid. In other words, conservatives see tax credits, and lower taxes for lower incomes and higher taxes for higher incomes, as simply redistribution with no effect on the underlying, before-tax, wages.
But the underlying wages are affected by policy. For example, policies that help maintain full employment by managing aggregate demand levels in the economy will result in a tighter labor supply than it might have otherwise. This will cause average worker's (before tax)wages to rise, narrowing the gap between high and low income-earners.
Because a narrowing of this gap has the same demand-inducing effect as progressive tax rates, it would mean that taxes no longer need to be as progressive. In other words, the liberal progressive policy leads us closer to the ideal conservative vision of the economy.
Meanwhile, conservatives would assume that those higher average wages would be there anyway, (as a result of the free market), even if liberal progressive policies hadn't been in place. This is the same philosophy used now when conservatives assume that the current stagnant wages and massive income inequality, (also present in the Gilded Age and Great Depression,) are not a result of the dismantling of progressive policies.