There is absolutely an ever-growing gap between socioeconomic classes in the United States today. The distance between the rich and the poor has widened significantly in the post 9-11 era. Of course, one could simply blame capitalism for the economic class system. Capitalism is certainly not the most fair system, but one could argue that it is the most preferable for the most amount of people in terms of standard of living, social mobility, etc -- and one could also argue that capitalism (and a free market economy, in general) are natural off-shoots of democracy. Although there is a reasonable amount of truth to that, it is by no means an iron-clad rule.
To attempt to address your second question, I do believe that the republican economic policies do have a very negative effect on the poor and working class in the United States. However it's not quite so simple that you could say "republicans cause social injustice." The conservative economic view is that we should lower taxes (for all, however the ultra-rich are who benefit the most), cut spending on domestic programs, and privatize specific programs such as health care, social security etc.
Unfortunately many time the poor are duped into believing that lower taxes automatically are better because they have a few extra bucks in their paycheck. This isn't necessarily the case. Most working class people see very little return from a tax break and are mostly hurt by the cuts in spending for government programs such as education, health care, child care, etc. So in the long run, working class citizens will have to spend more money than they are saving because of a tax break.
The other economic misconception that conversatives tend to believe is that the Reagan "trickle down" theory actually works. This is based on the idea that if the rich are granted a tax break, they will go out and spend the money they saved on a service or product which will in turn create more jobs and filter money down to the working class. However, the problem with this theory is that with the increased outsourcing of jobs and the influx of non-American goods, the only people benefitting from the rich spending their money, are the shareholders of the large corporations in which the money was spent. In turn, the rich are just making the rich richer. And with corporations making increased profits, they will continue to give financial support to Republican candidates so that they can vote favorably towards their particular corporation's industry.
So basically to make a long story short, the Republican economic policy has certainly widened the gap between the rich and the poor, and one could certainly argue that this gap is a form of, or at least directly causes, social injustice.