1) The 2004 poverty rate in the US was 12.7%, an increase from 12.5% the previous year The US Census Bureau has more information on poverty at their web site. 12.7% isn't just a nominal percentage, it's millions of people - adults and children.
2) In many areas of the country, working full-time at the minimum wage still isn't enough to support a family. Use the calculator here to determine how much a family of four needs to live a decent life, and compare that to the income from a two-worker minimum wage family. If a two-parent household worked full-time, all year at minimum wage they would make $21,424 ($5.15/hr * 2080 hours/yr * 2). In Cincinnati, a livable family budget is about $45,000/yr; in Boston it's close to $65,000/yr; in Los Angeles it's $48,000/yr. In rural Arkansas it's $32,000/yr.
3) Big companies that rely on lower wage jobs – services, fast-food, etc – could most likely afford a labor rate increase. For example, in 2005 McDonald’s had $2.6 billion in net profit. Only 17% of small businesses say that raising the minimum wage would have a negative impact on them (June 2006 issue of Fortune Small Business, not yet online – but taken from here).
4) 83% of the population favor an increase in the minimum wage.
5) Fair wages are moral, and the Catholic church has advocated them for a while now. For example, from the encyclical Mater et Magistra published in 1961 by Pope John XXIII:
We therefore consider it Our duty to reaffirm that the remuneration of work is not something that can be left to the laws of the marketplace; nor should it be a decision left to the will of the more powerful. It must be determined in accordance with justice and equity; which means that workers must be paid a wage which allows them to live a truly human life and to fulfill their family obligations in a worthy manner.