One impediment to being like LBJ is, perhaps, the fact that LBJ's use of power has been systematically underrecognized for a variety of reasons, many of which are discussed in the new (fourth) volume of Robert Caro's biography. Garry Wills, reviewing at the New York Review of Books, focuses on the RFK-LBJ relationship:
To understand the sheer wastefulness of this conflict, try to imagine the impossible. What if the two men, instead of bringing out the worst, had played to the best in each other? Suppose Bobby had recognized his brother’s need of Johnson in 1960, had helped capitalize on his resources in the South, and had made him an effective partner in Jack’s administration, instead of a sullen man isolated in his discontent. Would some of the effective legislation of Johnson’s turn in office have been accomplished earlier? Or suppose that Johnson, open to the alternative insights of Bobby, had seen the force of objections to the Vietnam War before he floundered so deep into that Big Muddy. What if he had won over the young people who ended up chanting outside the White House, “Hey, hey, LBJ/How many kids did you kill today?”
Or, for that matter, even if Bobby Kennedy didn't want to work with LBJ, imagine if he had taken a more temperate view of Johnson's existence. As Caro notes, it was partly because of Kennedy's animus against Johnson that the domestic accomplishments of the Johnson presidency have been often underrated. For Kennedy, Johnson was the usurper of the legacy that should rightfully have been his brother's; per the younger Kennedy's account, Johnson never even should have been vice-president--he just pounced on a perfunctory invitation. "These accounts are given weight by many historians because of Robert Kennedy's repeated, and emphatic, reiterations of them, and because of the acceptance of those reiterations as accurate, and the restatement of them in books and articles by Arthur Schlesinger, whose writings on John and Robert Kennedy have for decades set the template for the image of the two brothers in history," writes Caro.
The effect was to help delegitimate LBJ's presidency and marginalize his accomplishments. Maybe that would have happened anyway, given Vietnam, and given LBJ's own flaws. But the cost was that if you don't take LBJ seriously, you'd be hard-pressed to explain how he passed so much legislation, much less to replicate his use of power. In five years he signed dozens of laws that advanced civil rights, environmental stewardship, public education, and so on--priorities that JFK shared, but would likely have struggled to get into law.