The New York Times reports the identity of one of the male lawmakers named in Gillibrand's book.
Blog Briefing Room
The potential changes are in response to a fence jumper reaching the building on Friday.
Omar J. Gonzalez, 42, reportedly had to retire because of a disability.
“I know there are contracts but this has gone on too long," she said.
"He could have had a body bomb; he could have had a vest on,” King said.
An intruder jumped the fence at the executive mansion shortly after President Obama departed.
The intruder drove up to the White House gate and pulled into the vehicle screening area.
NBC says a report ruling out federal charges against New Jersey governor was incorrect.
Sen. Dianne Feinstein and Reps. Mike Rogers, Peter King among guests.