Traditionally, the Republican platform has been lower taxes for everyone, rich, middle-class, and poor alike. Both Reagan's and Bush's tax cuts benefited almost all workers. Recently, however, some Republicans, including several of the leading candidates, have been complaining about the poor not paying enough taxes. Specifically, they say it is a big problem that 47% of Americans do not pay income tax. In some ways, I see their point. If people are receiving social services but not paying for them, there is nothing to stop them from continuing to vote for more and more government services, ad infinitum. However, the working poor already pay quite a bit of tax: payroll taxes, sales taxes, and gas taxes. Saying they need to pay more tax--while also calling for less overall spending on social programs--is an extremely tone-deaf stance that could cost Republicans a lot of working class votes. It smacks of contempt for the poor and class warfare in reverse.
When I worked as an AmeriCorps volunteer three years ago, I made $900 a month before taxes. The $65 or so in payroll taxes that they took out of each month's pay was a huge hit. My AmeriCorps director encouraged me and my fellow volunteers to go on food stamps. I desperately wanted to avoid relying on government assistance, and managed to make it work--but that was possible only because I did not have to pay income taxes. If Republicans did raise taxes on the poor, many of them would probably just use more food stamps and welfare money. The end result would be more taxes and more government spending--which doesn't seem like what the Republicans want.
In fact, here is a Businessweek article by a conservative economist that calls for expanding the earned income tax credit in order to reduce dependence on welfare.
There is still, however, the issue of people receiving social services without paying for them. I can think of two ways to address this issue without raising taxes on the poor. One, limit the child tax credit, WIC, and similar programs so that credits/benefits gradually phase out after two children or so. At some point, parents have to be responsible for supporting their own children, and the government should not subsidize (i.e. encourage) people who have large numbers of children that they cannot support. Secondly, eliminate the payroll tax, replacing the worker's portion with an additional equivalent amount of income tax. I've already discussed the evils of the payroll tax (it's regressive, it often goes unnoticed, it discourages job growth by taxing hiring). Plus, that way, when Congress wants to cut or raise income taxes, every worker will feel the effects to some degree. Hopefully people will start to realize that they have to pay more to get more, and that tax cuts can help people at all income levels not just the rich.