Sanhedrin 12B

כי אכלו את הפסח בלא ככתוב כי התפלל חזקיהו עליהם לאמר ה׳ הטוב יכפר בעד״.

yet they ate the Paschal lamb not as is written. For Hezekiah had prayed for them, saying: May the good Lord pardon everyone who sets his heart to seek God…though he not be cleansed according to the purification that pertains to sacred items” (II Chronicles 30:18–19).

רבי שמעון אומר: אם מפני הטומאה עיברוה, מעוברת. אלא מפני מה ביקש רחמים על עצמו? שאין מעברין אלא אדר, והוא עיבר ניסן בניסן. רבי שמעון בן יהודה אומר משום רבי שמעון: מפני שהשיא את ישראל לעשות פסח שני.

R' Shimon says: If the court intercalated the year due to ritual impurity, it is indeed intercalated. But if ritual impurity is ultimately a legitimate reason for intercalating the year, for what reason did Hezekiah request compassion for himself? Because the court may intercalate only the month of Adar, and he intercalated the month of Nisan during the month of Nisan itself. R' Shimon ben Yehuda says in the name of R' Shimon: The incident did not involve the intercalation of the year; rather he appealed for mercy because he encouraged the Jewish people to bypass the standard first Pesaḥ and instead to perform the second Pesaḥ.

אמר מר: רבי יהודה אומר: מעברין. אלמא, אית ליה לרבי יהודה: טומאה דחויה היא בציבור.

Having quoted the Tosefta in its entirety, the Talmud now clarifies several of its details. The Master said above: R' Yehuda says: The court may intercalate the year due to ritual impurity, in order to delay the Paschal offerings, so that the people can perform them in a state of purity. Apparently, R' Yehuda holds that the prohibition against performing the Temple service in a state of ritual impurity is merely overridden in cases involving the public. Although the offerings may be brought when most of the public is in a state of impurity, this course of action is not ideally permitted; one must attempt to find another way to perform the offerings in purity.