Bris Milah is performed only on a completely healthy baby. We have discussed here and here, in general terms, what would delay a bris. In these next few blog posts, I intend to translate portions from the book Bris Avos (Shabtai Lifshitz), Chapter 9, "The Law of a Baby Who is Ready to be Circumcised, and Which is Not Ready to be Circumcised." The book was first published in Elul 5673 - a few months shy of 100 years ago (it is now Tammuz 5773). It was reprinted by the author's grandson in 1969.
We do not circumcise a child who has even the slightest indication of illness, on account of our concern for life (Maimonides – chapter one, laws of Milah, as well as the Tur 263:1). They were careful to say even the "slightest indication" (חשש), even if it's not completely apparent. For example, even if he cries excessively, we would not circumcise him yet. The Pischei Teshuvah wrote that even if the baby's belly button was not cared for properly, and it bleeds, we do not circumcise him until he has strengthened, healed and has recovered the lost blood from the bellybutton. In my humble opinion, the baby is not to be circumcised without asking doctors or experts [if he is ready].
The author is making our concern for the baby's health paramount. Obviously the bris milah carries its own risks, but this is the price of this mitzvah.
Having said that, when the bris milah is performed properly on a completely healthy baby, the procedure is usually a smooth one, and baby returns to his normal routine once he is in his parents' arms. Anything out of the ordinary can be a cause for delay. [Normal physiological jaundice need not necessarily be a cause for delay... See here]