I think that's not an unfair statement. If the GOP made a head-on attack to change Rule XXII, they would have its language to contend with.
RULE XXII
PRECEDENCE OF MOTIONS2. Notwithstanding the provisions of rule II or rule IV or any other rule of the Senate, at any time a motion signed by sixteen Senators, to bring to a close the debate upon any measure, motion, other matter pending before the Senate, or the unfinished business, is presented to the Senate, the Presiding Officer, or clerk at the direction of the Presiding Officer, shall at once state the motion to the Senate, and one hour after the Senate meets on the following calendar day but one, he shall lay the motion before the Senate and direct that the clerk call the roll, and upon the ascertainment that a quorum is present, the Presiding Officer shall, without debate, submit to the Senate by a yea-and-nay vote the question:
"Is it the sense of the Senate that the debate shall be brought to a close?" And if that question shall be decided in the affirmative by three-fifths of the Senators duly chosen and sworn -- except on a measure or motion to amend the Senate rules, in which case the necessary affirmative vote shall be two-thirds of the Senators present and voting -- then said measure, motion, or other matter pending before the Senate, or the unfinished business, shall be the unfinished business to the exclusion of all other business until disposed of.
http://rules.senate.gov/senaterules/menu.htm <-- All the Rules
So, the conventional methods to bring debate to a close are unanimous consent, or to use this rule, Rule XXII, cloture. But what if cloture is never called for? What would that process look like?
IIRC the vote proceeds to a straight up or down vote, which is all the (R)s want.