The truth is -- sort of, but not really. Yes, LBJ was his own congressional liaison. He knew members intimately --their personalities, personal and private behaviors, and pressure points. After all, he had been "Master of the Senate" for eight years and had been in Congress since 1937. Until Obama's election, only two presidents in the previous century had gone directly from Congress to the White House --Warren Harding and John F. Kennedy. LBJ also had large Democratic majorities from which to corral the needed votes.
No other president in our lifetimes had as much knowledge of Congress and its members as LBJ. Yet they all had congressional liaison offices that offered perks and made threats -- the carrots and sticks the pundits think Obama should use more assertively. Sometimes they won; sometimes they lost. Here's an interesting chart showing congressional voting where the president had an announced position on a matter up through 2006. As you can see, LBJ had an astonishing 82.2% success rate during his presidency. But there are anomalies: Eisenhower had even higher ratings his first two years, when the GOP controlled Congress. So did Clinton his first two years, before the GOP gained congressional majorities.
I haven't searched the literature, but here's an academic study from 2009 on what accounts for presidential success in Congress:
Overall, for Presidents Clinton and Bush, presidential popularity, economic conditions and control of Congress have shown to be significant in determining presidential success in Congress. Party unity was shown to not be significant, contrary to past theories and a hypothesis of this study. Control of Congress was demonstrated to be the strongest indicator of success, followed by popularity, and then by economic conditions.These results mean that arm-twisting works when your party controls Congress, your popularity is high, and the economy is humming. An in today's supermajoritarian Senate, "control" means 60 votes. In these circumstances, Obama has an uphill fight.