In 1841, when the Democratic minority hoped to block a bank bill promoted by Kentucky Senator Henry Clay, he threatened to change Senate rules to allow the majority to close debate. Missouri Senator Thomas Hart Benton rebuked Clay for trying to stifle the Senate's right to unlimited debate.
Three quarters of a century later, in 1917, senators adopted a rule (Rule 22), at the urging President Woodrow Wilson, that allowed the Senate to end a debate with a two-thirds majority vote, a device known as "cloture." The new Senate rule was first put to the test in 1919, when the Senate invoked cloture to end a filibuster against the Treaty of Versailles.

But we know the filibuster best from its role during the Civil Rights Era.

Even with the new cloture rule, filibusters remained an effective means to block legislation, since a two-thirds vote is difficult to obtain. Over the next five decades, the Senate occasionally tried to invoke cloture, but usually failed to gain the necessary two-thirds vote. Filibusters were particularly useful to Southern senators who sought to block civil rights legislation, including anti-lynching legislation, until cloture was invoked after a fifty-seven day filibuster against the Civil Right Act of 1964. In 1975, the Senate reduced the number of votes required for cloture from two-thirds to three-fifths, or sixty of the current one hundred senators.

Notice that the reduction to sixty was a reform of the Watergate Babies.  

But, you don't have to physically stand there and talk if you are willing to engage in a constant game of noting the absence of quorum.  Otherwise, the Senate has to be in attendance at all times to prevent the absence of a quorum.  

The absence of a quorum occurs when it is officially demonstrated that the number of Members required to conduct business is not present on the House or Senate floor. If a quorum call or roll-call vote demonstrates that a quorum is not present, no further debate or other business may be transacted, except a motion to adjourn or a motion to request or require the attendance of absent Members. In the House, the chair can count the Members who are on the floor to determine if a quorum is present. The presiding officer in the Senate usually does not have this authority.

In the Senate, a quorum call is called off by unanimous consent before all Senators' names have been called. The absence of quorum has not been demonstrated, and the Senate may resume its business.

A small handful of senators can effectively filibuster just by continuously noting the absence of a quorum and forcing roll call votes.  There is no way to force the Republicans to stand up there all night reading from the phonebook.  

There never was.  They chose to speak back during the Civil Rights Era because they were grandstanding.  

The only way to punish the GOP for obstruction in the Senate is to do what was done in 1964.  Set aside all other Senate business for 57 days (or however long it takes) and complain loudly to the American people.