The minimum-wage advocates who have thought much about it (of course, many haven't) usually have in mind some kind of monopsony model - that is, they assume a market in which employers have some degree of monopoly buying power. Under monopsony, wages can in theory be increased within a certain range with no reduction (and maybe even an increase) in employment. But if the wage rises above a critical point, then disemployment kicks in. Thus, a believer in the monopsony model can consistently favor small increases in the minimum wage while still opposing large ones.
In a product market, a monopolist will charge a price that is too high. In theory, the government can improve welfare by setting a price ceiling. The case of a labor market monopsonist (only one employer), the symmetrical argument is that a wage floor can improve welfare.
It's hard to think of any real-world labor market monopsonists. Perhaps there is monopolistic competition--many firms, each with some price-setting and wage-setting power. However, in a monopolistically competitive market, price ceilings (and presumably wage floors) do not increase output and employment. Instead, they drive firms out of business.
In any case, I expect that we are reaching the point in the business cycle where wage growth picks up. If there is a problem with wages being too low, that problem will have gone away by inauguration day, and perhaps sooner.
For Discussion. If you were advising Senator Kerry, what economic issues would you recommend using in his campaign?