kiddush hachodesh - What is the source for Hillel’s having included an expiration date in the calendar?

It’s often said that when Hillel instituted the current calendar, he set an “expiration date” of 6000 AM; at that point the calendar would be invalid. Since Mashiach presumably will come by then (as per Sanhedrin 97a et. al.) the calendar doesn’t need to run farther than that.

As often as I’ve heard this repeated, I’ve yet to find a concrete source for it. @Shalom asks a question here regarding the calendar post-6000, and @DanielBilar asks here whether the existence of a month hangs on its sanctification and thus if we even can have a calendar post-6000, barring Mashiach’s imminent arrival. In discussing this point with others in the comments to the latter question, we arrived at the Rambam, Hilchos Kiddush HaChodesh 5:2ff who says nothing about sanctification, merely that we can use a calendar if there’s no Sanhedrin around to sanctify the month, and a reference to the Netziv and other poskim, but it doesn’t have any sources.

Does anyone know where I can find someone who says this explicitly, that the calendar’s existence hangs on the fact that Hillel and his Beis Din sanctified the calendar for the following 1600 years, only up to the year 6000 in anticipation of Mashiach’s arrival?

Answer

You write that:

It’s often said that when Hillel instituted the current calendar, he set an “expiration date” of 6000 AM; at that point the calendar would be invalid. Since Mashiach presumably will come by then (as per Sanhedrin 97a et. al.) the calendar doesn’t need to run farther than that.

I think that this is a misunderstanding. What is actually said (as we shall see) is that Hillel sanctified all of the months until Mashiach's arrival, without specifying when that would be.

When this is coupled with the assumption that Mashiach will come by the year 6000, people may say that Hillel fixed the calendar until that time, but by no means is he said to have explicitly given an expiration date.

The earliest source I find for the assertion that Hillel pre-sanctified the months is Ramban in his glosses to Sefer HaMitzvot, Aseh 153:

רבי הלל הנשיא בנו של רבי יהודה הנשיא תקן חשבון העבור הוא קדוש חדשים ועיבור שנים הראויים להתעבר לפי מנינו עד שיבוא אליהו ז"ל ונחזור על פי הראיה בב"ד הגדול והקדוש אמן במהרה בימינו יהיה

R. Hillel the Prince, son of R. Yehudah the Prince, fixed the calculation of the ibbur, that is the sanctification of the months and the intercalation of the years which ought to be intercalated according to his count, until Eliyahu comes and we return to [the system] of observation in front of the great and holy court. Amen, may it be speedily in our days!

So, if for whatever reason, Mashiach has not arrived by the end of the sixth millenium, Hillel's pre-sanctification of each and every month will just keep going for as long as necessary.

(Of course, there may be other reasons why a reform of the calendar may be needed in the event of Mashiach's late arrival, not least the issues with the slowly shifting date of Pesach with respect to the solar calendar, but there would seem to be no need for a renewed sanctification of the months after the year 6000, even if one accepts Ramban's position over that of Rambam.)