As a factual backdrop for the ongoing arguments about whether or how much to raise the minimum wage, a useful starting point is the most recent version of the annual report from the US Bureau of Labor Statistics on "Characteristics of Minimum Wage Workers, 2016" (published April 2017). It begins:
"In 2016, 79.9 million workers age 16 and older in the United States were paid at hourly rates, representing 58.7 percent of all wage and salary workers. Among those paid by the hour, 701,000 workers earned exactly the prevailing federal minimum wage of $7.25 per hour. About 1.5 million had wages below the federal minimum. Together, these 2.2 million workers with wages at or below the federal minimum made up 2.7 percent of all hourly paid workers. The percentage of hourly paid workers earning the prevailing federal minimum wage or less declined from 3.3 percent in 2015 to 2.7 percent in 2016. This remains well below the percentage of 13.4 recorded in 1979, when data were first collected on a regular basis ..." 
The report is mostly a series of tables, which the interested reader will want to pick through. Here are some highlights from the 2016 data as selected by BLS (parenthetical references to specific supporting tables omitted):
Age. Minimum wage workers tend to be young. Although workers under age 25 represented only about one-fifth of hourly paid workers, they made up about half of those paid the federal minimum wage or less. Among employed teenagers (ages 16 to 19) paid by the hour, about 10 percent earned the minimum wage or less, compared with about 2 percent of workers age 25 and older.  ... 
Education. Among hourly paid workers age 16 and older, about 5 percent of those without a high school diploma earned the federal minimum wage or less, compared with about 3 percent of those who had a high school diploma (with no college), 3 percent of those with some college or an associate degree, and about 2 percent of college graduates. ... 
Full- and part-time status. About 6 percent of part-time workers (persons who usually work fewer than 35 hours per week) were paid the federal minimum wage or less, compared with about 2 percent of full-time workers. 
Occupation. Among major occupational groups, the highest percentage of hourly paid workers earning at or below the federal minimum wage was in service occupations, at about 7 percent. Two-thirds of workers earning the minimum wage or less in 2016 were employed in service occupations, mostly in food preparation and serving related jobs.
Industry. The industry with the highest percentage of workers earning hourly wages at or below the federal minimum wage was leisure and hospitality (about 13 percent). Three-fifths of all workers paid at or below the federal minimum wage were employed in this industry, almost entirely in restaurants and other food services. For many of these workers, tips may supplement the hourly wages received. 
State of residence. The states with the highest percentages of hourly paid workers earning at or below the federal minimum wage were Idaho, Kentucky, Louisiana, Mississippi, and South Carolina (all were at or about 5 percent). The states with the lowest percentages of hourly paid workers earning at or below the federal minimum wage were in the West: Alaska, California, and Oregon (all were 1 percent or less). It should be noted that many states have minimum wage laws establishing standards that exceed the federal minimum wage.
I was also struck by this regional breakdown: of those being paid at or below the federal minimum wage in 2016, 48.5% lived in the South, 21.6% in the Midwest, 16.7% in the Northeast, and 13.3% in the West. The report doesn't have a breakdown of  minimum wage workers by urban and nonurban areas, but I suspect those differences would be fairly large, too.

As long as we're laying down a fact base, here are a few figures, Here are the share of hourly workers (that is, not all workers, but that proportion of workers paid hourly) who receive the minimum wage, from the FRED website run by the Federal Reserve Bank of St. Louis


And here are  a couple of figures put together earlier this year by Drew DeSilver of Pew Research in a short report called "5 facts about the the minimum wage" (January 4, 2017). Here's a state map and a list of state minimum wages giving a sense of which states have a higher state-level minimum wage, and the level of those minimum wages.

Finally, here's a figure from DeSilver showing the evolution of the nominal and real federal minimum wage over time. 

I'm of course well aware that few people will dramatically alter their opinion about the minimum wage based on these kinds of facts.

For example, some will look at the variation across states in minimum wage levels and see it as a sest of differences that are appropriate given the differences in wages and political values across the US states; others will see the difference as a reason the federal government needs to step in and raise minimum wages in states that have been reluctant to do so. As another example, some will look at the figure showing that 2.7% of hourly workers are paid the minimum wage, with the majority of the the "leisure and hospitality" industry like restaurants and food services, and view that as an argument that there's not much reason to raise the minimum wage ("a raise would affect only a narrow slice of workers, most of them young and in food service") while others will look at the same data and view it as a strong justification for  a substantially higher minimum wage ("the low share of hourly workers receiving the hourly minimum wage means it is overdue for a raise").

Still, having an agreed-upon fact base may at least set boundaries of realism that rule out some of the more extreme claims, and in that way help to  focus the arguments.