The suit, which accuses the Federal Bureau of Prisons of lying about conditions inside the jail, comes after days of protests, which began after inmates drew attention to their plight by making noise that could be heard on the streets below the jail.
She said senior officials at the jail were "indifferent" to the problems during her tour even as guards complained to her of the cold.
The incident follows a weekend of protests at the detention center, where inmates complained of having no heat in their cells for days after a fire on January 27 left a large portion of the facility without electricity. "Where's the president on this? They're humans, they're not animals".
Murchison's son Desmond, who she said has been awaiting trial for a year at the Sunset Park jail, shouted to his mother through metal grates on Sunday.
But despite the show of support from local officials, some family members said they wanted authorities to do more to stand up for their incarcerated relatives. Several protesters came running out minutes later to cover their faces in water and milk. Meetings between attorneys and clients today were canceled after a reported bomb threat. "Those individuals with medical conditions, unfortunately, their medical conditions are not being addressed", she said.
Bob McGee, a spokesman for power company Con Edison, said they are ready to reconnect the electricity once repairs are completed.
Con Edison crews started working Sunday morning to fix the power. It was restored Sunday evening.
A spokesperson for MDC said in part, "Inmates have hot water for showers and hot water in the sinks in the cell". He said the warden told him 600 blankets from the city had been distributed.
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The updates Sunday did little to stem the anger outside the prison, where protesters once again gathered. "We've told the Federal Bureau of Prisons the supplies are coming - whether they like it or not".
"I want my children to understand that we can absolutely teach about the injustices, but to really be change agents against these injustices you have to get out there and move with the people", Smith said. "This has gone on for far too long". The woman, crying and upset, tried to get into the facility, where visits have been stopped. "It is essential that BOP ensure that no detainee be subjected to retaliation for peacefully protesting this inhumane treatment".
The Federal Bureau of Prisons did not immediately respond to a request for comment on the disparity between its account and the attorneys' accounts.
"The big power issue that has caused significant problems this week resulted from the fire on [last] Sunday, but they may have been having other electrical problems before that", Patton said. The power problems have also meant inmates can not easily call family or lawyers nor get any needed medication refilled, lawyers said.
One US representative who visited the facility on Saturday told CNN affiliate WPIX that the temperature was as low as 49 degrees in the detention center.
Officials said power was restored at the federal detention center Sunday night, CBS News reported.