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Marisa Rodriguez was paralyzed in the accident.

McALLEN, Texas, (CNN) -- Saying tires made by Bridgestone/Firestone have "killed more people than Timothy McVeigh did in the Oklahoma City bombing," an attorney for the plaintiffs in a $1 billion lawsuit against the company urged the jury Tuesday to hold the company liable for the wreck that left a woman in a wheelchair.

Jurors began deliberations at 3:30 p.m. and retired for the evening less than two hours later without reaching a verdict in a case that has generated new attention on allegations of defects in Firestone tires. The attorneys made their closing arguments under pressure from Judge Filemon Vela to bring the trial to a close.

The family of Marisa Rodriguez is suing Bridgestone/Firestone for $1 billion over a March 9, 2000, accident that left Rodriguez, 41, wheelchair-bound. The accident occurred on a Mexican highway when the tread separated from a tire on her family's Ford Explorer and the vehicle overturned.

During closing arguments, plaintiffs' attorney Mikal Watts made the comparison between the tires and McVeigh, who killed 168 people when he bombed the Murrah Federal Building in Oklahoma City in 1995.

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Watts asked the jurors to consider "what type of message ... you want to send to Firestone and companies that do things like Firestone has done."

Defense attorney Scott Edwards argued the tire that blew out on the Rodriguez' Explorer "failed for other reasons, not design problems."

The defense postulated that the tire had picked up a foreign object from the road some 1,000 to 2,000 miles before the blowout that caused the tread separation. And Edwards told the jury that Ford was at fault for the fact the vehicle rolled over when the tire blew out.

"Ford should be 100 percent responsible for the injuries suffered by this family," he said.

The family reached an out-of-court settlement with Ford in July for a reported $6 million.

Throughout the trial, attorneys for Bridgestone/Firestone have called witnesses who raised questions about the design of the Ford Explorer.

The accident involving the Rodriguez family occurred five months before Firestone announced the recall of 6.5 million 15-inch Wilderness AT, ATX and ATX II tires made at the company's plant in Decatur, Illinois, where the tire at issue was made.

The National Highway Traffic Safety Administration has documented 203 deaths and more than 700 injuries linked to tread separation rollover accidents involving Firestone tires and Ford Explorers.

Ford blames the problem on faulty tires. Firestone blames it on design flaws in the popular Explorer. The fallout led the companies to sever their century-old business relationship.

During testimony for the defense Monday, Bridgestone/Firestone's expert James Gardner told the jury the tire on the Rodriguez's Explorer suffered an impact injury about 4,000 miles before the accident. The tire likely hit a baseball-sized object, possibly a rock, which broke the steel filaments inside the tire, said Gardner.

Gardner also testified that drivers should notice a vibration in the ride of the vehicle if a tire is separating, which signals to them there is a problem with the tire. But he said a majority of Explorer drivers do not notice a vibration on tires with separations on the rear of the vehicle.

"There's something in that vehicle that's masking the separation," said Gardner.

Watts disputed Gardner's status as an independent witness in questioning Monday.

Gardner, who worked as a tire investigator for the FBI in the World Trade Center and Oklahoma City bombings, retired as director of product analysis for Bridgestone/Firestone last September and has since worked as an independent tire expert.

Gardner testified that under his contract Bridgestone/Firestone would retain him for 950 hours a year for a period of three years at $210 an hour -- nearly $200,000 a year.

Watts then questioned Gardner on why he would testify in this case that the Ford Explorer had a propensity to roll over, when in seven past cases cited in court -- before the Ford-Firestone relationship began to sour -- he testified for Bridgestone/Firestone that the Explorer "does not have an unreasonable propensity to roll over."

Gardner answered he had never considered the handling of the Explorer to be the problem until the recall, when he began examining the number of complaints in which the driver of the Explorer lost control.

-- CNN Detroit's Carol Yancho contributed to this report.