Yes there is a time limit between the filing of a cloture petition and the actual cloture vote.
The procedure for "invoking cloture," or ending a filibuster, is as follows:
* A minimum of sixteen senators must sign a petition for cloture.
* The petition for cloture may be presented by interrupting another Senator's speech.
* The Senate's clerk reads the petition.
* The cloture petition is ignored for one full day during which the Senate is sitting (If the petition is filed on a Friday, it is ignored until Tuesday, assuming that the Senate did not sit on Saturday or Sunday.)
* On the second calendar day during which the Senate sits after the presentation of the petition, after the Senate has been sitting for one hour, a "quorum call" is undertaken to ensure that a majority of the Senators are present.
* The President or President pro tempore presents the petition.
* The Senate votes on the petition; three-fifths of the whole number of Senators (sixty with no vacancies) is the required majority; however, when cloture is invoked on a question of changing the rules of the Senate, two-thirds of the Senators voting (not necessarily two-thirds of all Senators) is the requisite majority.
After cloture has been invoked, the following restrictions apply:
* No more than thirty hours of debate may occur.
* No Senator may speak for more than one hour.
* No amendments may be moved unless they were filed on the day in between the presentation of the petition and the actual cloture vote.
* All amendments must be relevant to the debate.
* Certain debates on procedure are not permissible.
* The presiding officer gains additional power in controlling debate.
* No other matters may be considered until the question upon which cloture was invoked is disposed of.