Pedro de la Rosa says HRT will struggle to make the 107 per cent qualifying cut-off for the United States Grand Prix if the new Austin circuit's grip levels do not improve.
Both de la Rosa and team-mate Narain Karthikeyan struggled badly during Friday practice, during which they were unable to 'switch on' their tyres.
The veteran's best lap in the afternoon session was 6.375 seconds slower than pacesetter Sebastian Vettel, a mark of 106.892 per cent.
Karthikeyan, who sat out the first session to allow Ma Qing Hua to drive and completed only 20 laps in the afternoon, lapped at 107.569 per cent of the fastest time.
HRT has had the pace to qualify for every race since Australia, where both drivers were unable to start.
"I'm not confident," de la Rosa told AUTOSPORT. "It is marginal.
"It will depend on whether we manage to get into the tyre-temperature window, which we were definitely not getting on Friday. This is our biggest issue.
"We are slower than at other tracks mainly because we are not working the tyres at all, not the prime nor the option. They are just like new after a 10-lap run.
"The track evolution was so low because there is no tyre wear, therefore the asphalt doesn't pick up rubber.
"That makes me think that Saturday is going to be difficult for us. If the track evolution proves to be similar to Friday, then we will have problems and it's going to be a tough qually for us."
De la Rosa accepted that if things did not improve, HRT might be forced to approach qualifying as a single long-run in the hope of building enough tyre temperature to find the grip.
"It's looking like in Q1, put as much fuel as you can in and run to the flag," he said. "But hopefully I'm wrong.
"Hopefully there is slightly more rubber on the track and we manage to switch the tyres on so we don't have to do that."
The 41-year-old Spaniard also insisted that his lack of running, completing just 29 laps on Friday, was not because of financial problems.
He claimed that it was because more running was futile given the tyre-temperature problem.
"We had the tyre issue and we thought it was quite useless to run first thing in the sessions when the track was slippery," said de la Rosa.
"If we had tyres that switched on initially, then we should have run more."