Taft Hartley, Hank Kimball and Aldy Bledsoe are three dating-challenged, nuclear engineers who work for the San Onofre Nuclear Power Plant. Taft is obsessed with Da Vinci’s painting of the Mona Lisa, which has fascinated him since he was lost in the Louvre when he was a boy. Unfortunately, every woman he meets doesn’t measure up to Mona, including Dean Schwarma, a gorgeous, very sexy, college administrator who has the hots for him. Hank Kimball is one of the nicest guys on the planet, but inept around women. He’s really into Sergeant Caroline Ho, a campus police officer who thinks he’s a nut case. Aldy is just terrified of women, but it doesn’t stop him from his search for the perfect mate. When San Onofre closes suddenly, our heroes pool their resources to open a really inane dating service called Classy Lassies. When it flops, they begin to wonder if they’ll ever get dates or jobs. When Taft falls through the back of a spin dryer and ends up in the Time Travel café, a temporal way station where famous historical figures play poker and eat a lot of Taft’s mother’s recipe for guacamole, their lives changes inexorably.
While kibitzing during a high-stakes game among Julius Caesar, Harry Houdini, Grover Cleveland, Noah, Charlie Sheen and H.G. Welles, Taft wonders how each of them has one of the most beautiful women in the world draped over their shoulders, especially Grover Cleveland. Welles directs him to Gwen Helen of Rothchild, the temporal dating priestess of the universe, and the CEO of Dating History, an unusual dating service that matches historical figures with ordinary citizens, across all time periods. To Taft’s surprise, Gwen Helen offers him some start-up money and a franchise, the first ever given to a contemporary human.
Taft returns to his friends, with $100,000 in cash and the franchise. To their surprise, the next morning a stagecoach arrives with an installation team, and temporal transfer tubes are installed. Taft is then given computerized dating profiles on virtually everyone ever born on planet Earth – the ultimate Date-a-Base. Dating History is an overnight sensation – hundreds of love-starved men and women start dating famous historical figures such as Moses, Cleopatra, Helen of Troy, Samson, Babe Ruth and Marie Curie. They get international media attention – Taft goes on Jimmy Fallon with a Southern belle and her date – the actual Elvis, and everything is going well, even though Gwen Helen warns the three owners that they can’t date the clients, or travel back in time themselves. It would violate eleven temporary travel statutes. Relentlessly pursued by the over-sexed Dean Schwarma, Taft keeps her at bay by an offer of a free date with Beethoven. Hank is devastated when Sergeant Ho starts dating Samson, but that relationship fizzles when the strongman spends the night chasing after her girlfriend, Phyllis Stein.
However, Hank’s devastation is nothing compared to Taft’s discovery that someone is dating Mona Lisa. When Taft find out that it’s a mob boss, he resolves to rescue her, which he does with Hank and Aldy’s help. But a date for pie afterwards with Mona, the girl of his dreams, violates Gwen Helen’s admonition, and the pair find themselves on the run chased by Gwen Helen’s time police. Unfortunately, they decide to hide in a Dating History temporal transfer tube, which Hank and Aldy normally cleanse each night, making sure the tubes are empty and sending back any clients desirous of returning to their home time zones. When they cleanse Taft and Mona’s tube, the pair are suddenly transported back to 16th Century Italy – a potentially cataclysmic event that could destroy the space time continuum and kill Taft. Unaware of the danger, Taft winds up in Pisa, Italy with Mona, who seems to know every eligible bachelor in 16th Century Italy (it turns out she’s really a slut who can’t say no).
Hank, Aldy and Sergeant Ho follow Taft and Mona into the past, where they bring a mysterious figure to a duel between Taft and one of Mona’s suitors. That mysterious figure turns out to be Dean Schwarma, a fencing expert who saves Taft’s bacon and disarms the suitor. To return to the present, Taft is informed that they must get back to Pisa – their jumping off point. Taft reluctantly agrees, realizing that Mona isn’t the girl for him, since she’s having affairs with men and women all over Italy. For some reason, she also seems to be obsessed with bread sticks. He then realizes that Dean Schwarma is not the over-sexed administrator he thought but a woman who truly loves him. Meanwhile, Hank and Sergeant Ho are getting along swimmingly and Aldy rescues a serving maid who falls for him.
To get back to Pisa in time, our heroes are rescued by Leonardo di Vinci himself in one of his patented flying machines. Returning to Los Angeles, Taft, Hank and Aldy are immediately accosted by Gwen Helen, who revokes their franchise. However, the three couples are very happy and content on their own.
A few months later, they all journey to Paris and pay a visit to the Louvre, where they visit Mona Lisa’s portrait – which is a tad different – she’s still smiling, but now holding a breadstick.