Prosecutor Patrick Fitzgerald argued Thursday that McCarthy should be held without bail because she is in the United States illegally and if released could seek deportation to Ireland, which does not extradite defendants who could face life sentences without the possibility of parole.
Thompson has called McCarthy "an innocent person sitting in jail" and said she wouldn't seek deportation if she were released on bail.
"She wants to answer these charges and clear her name," Thompson said.
Immigration officials have said McCarthy entered the United States in 2002 from Ireland under a tourist program that allowed a 90-day stay.
The baby's parents, Nada Siddiqui and Sameer Sabir, told police McCarthy had been a nanny for their family for about six months.