How about Robert Taft and Mike Mansfield? Lyndon Johnson was preceded as Senate majority leader by the man known as "Mr. Republican" and followed by the good and decent Mansfield, who went on to be a good and decent ambassador to Japan under Presidents Jimmy Carter and Ronald Reagan. (When was the last time anyone thought of a senator as such a statesman that he or she could serve as ambassador to a key ally for more than a decade under presidents from both parties?)
The point is that the Senate as an institution is — or was — quite the work of genius, but its individual members, no matter how famous in their day, fade into background characters in presidential biographies. (And most presidential biographies don't really get read all that much.) Now the Senate itself is careening toward widespread contempt, as happened to its Roman predecessor even before the emperors turned it into a fancy advisory council.
Whether the decline began with the sliming of Robert Bork or the segregationist filibusters of civil rights legislation, the modern Senate has been on a downward spiral for some time, and even current Senate majority leader Mitch McConnell (R-Ky.), the Senate's most able leader of my lifetime, isn't shrewd enough to reverse the trajectory in the public's eyes. After another government shutdown, President Trump and others are pushing hard to make the apparently dysfunctional upper chamber a purely majoritarian place. McConnell resists this, knowing that the rights of the minority party are (or at least used to be) key impediments on the country rushing into dangerous waters.
What the Senate needs is an overhaul of its rules, one that preserves the rights of the minority in some cases — key legislation, for example, and perhaps appointments to the Supreme Court — while also reflecting the speed at which the world moves today. Simple majorities on appropriations and time limits on debate over minor nominees are two obvious reforms. They could be traded for agreement on the high court vacancies, formalizing the modern precedent established by McConnell of no nominations in an election year but consideration and votes on nominees from the year prior such as Anthony M. Kennedy. The same deal could also include changes to the "Byrd Rule," which gives the Senate parliamentarian broad sway over what is allowed under budget reconciliation — an extraconstitutional expansion of the parliamentarian's powers that makes sense only under a Cubist understanding of how the Senate is supposed to operate.
Now, with the shock of the shutdown very palpable, McConnell and his minority counterpart, Charles E. Schumer (D-N.Y.), should empower a small group of widely liked and respected members to fashion a package of reforms with the only guarantee being that their work product receive an up-or-down vote made effective by a simple majority.
The Senate's dysfunction is astonishing to Americans who have to make things actually run and who have to do their jobs to keep their jobs. Trump has shrewdly taken aim at the Senate's vulnerability as an issue. It would be best for both parties to head off change imposed from pressure from the outside with change organically orchestrated from within by those with care for the body and its original design.