There are numerous reasons why prisoners are viewed as "a political problem." The most immediate concern regarding prisoners is whether ex-felons should have their rights to vote restored. Some states have voted in favor of the measure, such as Florida, but have seen bureaucrats express reluctance over putting it into practice. Most recently, in Kentucky, the new governor, Andy Beshear, has just restored voting rights to 140,000 ex-convicts. If more ex-felons (many of whom tend to be people of color) have their voting rights restored, this would likely result in a shift in the political balance in many states—that is, states that are solidly Republican like Kentucky or swing-states like Florida, could soon favor the Democratic Party. Depending on one's perspective, this could be viewed as a problem or a great boon. Regardless of one's political affiliation, however, if the United States is committed to the notion that society should forgive ex-convicts after they serve their time, then it would make sense to restore their voting rights.
Another pressing political issue around prisoners is how they are exploited within the prison-industrial complex—that is, the rapid expansion of private and public prisons in the interests of helping businesses profit from supplying goods and services to convicts. Prisoners and prison staff require a slew of provisions—food, entertainment, bedding, and now IT access. Corporations that provide these provisions reap massive profits by selling these products and services to prisons. Critics of the prison-industrial complex—an expression taken from President Eisenhower's mention of "the military-industrial complex"—argue that the justice system has been complicit in filling prisons, particularly with people of color, in the interests of ensuring that corporations can supply them.
I would also argue that you should reconsider the view of prisoners being "a problem." Instead, the problem lies in how American society runs correctional facilities and in how we choose to reintegrate prisoners into society after their release. Many prisoners relapse into crime as a result of being unable to escape their circumstances—a problem that is exacerbated by the extreme difficulty of finding employment that pays more than minimum wage.
For further reading about the history of Western penal systems, consult Michel Foucault's Discipline and Punish: The Birth of the Prison (1975). For further reading about the complexities of the criminal justice system, particularly its inequities, consult Courtroom 302: A Year Behind the Scenes in an American Criminal Courthouse (2005) by Steve Bogira.