Followers of the recent health care debate with short memories might well have thought that it requires 60 votes to pass any non-financial law in the Senate. That's why the loss of their 60th vote, with Republican Scott Brown's surprise victory in the Massachusetts special election to replace Ted Kennedy, was so devastating to the Democrats. Only by arguably misusing a sneaky maneuver called "reconciliation" (which is intended for budget bills) were they able to pass their reform. Or at least it was widely considered to be sneaky. By contrast the right of Republicans to insist on a 60-vote majority was considered playing tough, but not dirty.
As recently as 2006, things were different. Or maybe only the parties were different. When Democrats briefly filibustered President George W. Bush's Supreme Court nominee, Samuel Alito, the legitimacy of using a filibuster to require 60 votes instead of a simple 51-vote majority was widely debated. Queasiness about using such a sneaky trick, with its tawdry history as the way Southerners prevented a Civil Rights bill for several generations, may well have scared away some Democrats. At any rate, a 55-vote Republican majority was considered more than enough to stop it. This is in contrast to the 59-vote Democratic majority that is now considered insufficient.