Formula 1 boss Ecclestone described negotiations as "an uphill struggle".
Steve Sexton, president of the Austin circuit, said: "Our funding is secured and construction is on schedule, so we don't understand these comments.
"He has expressed great interest in the Austin race and in expanding the F1 brand into the US."Continue reading the main story 2000-7: Indianapolis1989-91: Phoenix, Arizona1984: Dallas, Texas1982-88: Detroit, Michigan1981-82: Las Vegas, Nevada1976-83: Long Beach, California 1961-80: Watkins Glen, New York1960: Riverside, California1959: Sebring, Florida
Ecclestone said on Saturday: "Austin? I wouldn't want to put my money down that that will happen. I hope it will and we are doing our best to make it happen, but I wouldn't want to say 'yes'."
Tavo Hellmund, the man behind the Full Throttle Productions company which is staging the race in November 2012, said Ecclestone has been tolerant throughout the situation.
"Mr Ecclestone has been incredibly patient with the challenges here in Austin," said Hellmund.
"Full Throttle Productions has worked tirelessly to bring the US Grand Prix to the city.
"It is now the responsibility of the Circuit of the Americas to make this project happen before Mr Ecclestone's patience runs out."
The dispute comes after Bahrain's Crown Prince confirmed the Gulf state will be able to hold its grand prix next season after civil unrest caused this year's race to be cancelled.
The US Grand Prix in Austin is the first of two new US races, with the Grand Prix of America in New Jersey scheduled for 2013.