You have a right to free speech, but there's no obligation for the government to buy you a printing press. You have the right to bear arms, but the government doesn't have to give you guns.
But there's no right to counsel if you can't afford one and if the public defender's office is super-saturated to the point of craziness. Unfortunately, that only affects poor people, so it's been easy to ignore the problem. But an ACLU suit against New Orleans may change that.
New Orleans faces a “constitutional crisis”: Chronically underfunded public defenders are now being forced to turn away clients
Those accused of crimes in New Orleans have a legal right to counsel — in theory, at least
Good.
Charlie Pierce on the subject: http://www.esquire.com/news-politics/politics/news/a41261/new-orleans-public-defenders/