When they were not paying any heed to the arguments...
“But whoever disputes with you in this matter after what has come to you of knowledge, then say: Come let us call our sons and your sons and our women and your women and our near people and your near people, then let us be earnest in prayer, and pray for the curse of Allah on the liars. (3:61)” The Prophet (a.s) read this verse to the Christians and invited them for the imprecation (Mubahalah).
The need for imprecation arose because if the matter was closed just with discussions, they would turn back and say that they requested the Prophet (a.s) for a debate, but we were not satisfied with his arguments. There was only one alternative to challenge them for the imprecation. After the Mubahalah, they would have nothing to brag home about. Initially the Christians were scared about the prospect of an imprecation. But later they relented.
They asked the Prophet (a.s) to give them a day respite. Then they went back to their inn and had a long discussion between themselves. Everyone had his own opinion. Abū-Harithah said that if Muhammad (a.s) came tomorrow with his and lot of men in attendance, we can accept to go for imprecation with him. But if he came in humility with his children and the family members, we must refute to have imprecation with him!
After making the agreement for the imprecation, the Prophet (a.s) selected a place outside al-Madinah for the purpose. Salman al-Farisi prepared it by removing the grass and the weeds from the ground. Early next morning the Christians reached the venue of the imprecation. The Muhajirūn and Ansar too came to the ground. When the Prophet (a.s) learned that the Christians had reached the site, he called for `Ali, Fatimah, al-Hasan and al-Husayn (a.s).
Sa`d ibn Abi-Waqqas says: “When the Verse of Mubahalah (Imprecation) was revealed, the Prophet (a.s) called `Ali, Fatimah, Hasan and Husayn (a.s) and said, ‘O Allah!