Tubbs Jones, 58, was hospitalized Tuesday night after police pulled over her car and found her unconscious behind the wheel.
A Huron Hospital spokeswoman said Tubbs Jones had suffered an aneurysm that caused her to lose consciousness.
As news of Tubbs Jones' hospitalization - and several premature reports of her death - spread across Capitol Hill Wednesday, the congresswoman's staffers gathered in a closed-door meeting.
Ohio Rep. Dennis Kucinich said he and his wife would be leaving Washington to offer "comfort and support" to Tubbs Jones' family.
Police pulled over Tubbs Jones's car in Cleveland around 9 p.m. Tuesday after noticing that it was moving erratically. According to local news reports, the car started rolling again as an officer approached the door. Once the car stopped in a grassy field, police discovered the congresswoman -- unconscious but breathing - in the driver's seat.
The daughter of an airport skycap, Tubbs Jones attended law school at Case Western University and served as a judge and a prosecutor before being elected to Congress in 1998.
She was the first black woman to represent Ohio in the House and served, since 2007, as the chairwoman of the House Ethics Committee.
A strong supporter of Hillary Rodham Clinton, Tubbs Jones endorsed Barack Obama in June and was scheduled to attend next week's Democratic National Convention in Denver.