The play is by Pulitzer Prize-winning author Robert Schenkkan, who wrote The Kentucky Cycle" It covers the difficult years of transition after Johnson became president following the Kennedy assasination until his re-election, Here's an article by Sarah Rodman from the Boston Globe.
"For a character with such dimension, director Rauch and playwright Schenkkan wanted a very specific kind of actor, and both are big 'Breaking Bad' fans.
“'We thought: Who has not just the charisma to pull off LBJ, but the courage and the skill and the heart and the cojones?' says Rauch. “Bryan was obviously a really thrilling choice, and Robert and I were able to meet with him in his home. And to our unbelievable joy, he said yes!'”
"Cranston says he couldn’t turn it down, and after his wife read the script, she agreed. 'You have to,' she told him."
There is one particularly humorous nod to the future of Breaking Bad in the article (which was posted on August 31), for those looking for clues. The reporter notes how problems are starting to get pretty bad for Cranston's character, Walter White. "Cranston laughs and intones mock-ominously, 'It gets worse before it gets worser.'”
Opposite Cranston in the picture below is Michael McKean who plays J. Edgar Hoover.