Certainly some of the parallels are coincidental. It is unlikely, for example, that the writers knew Mr. Obama had an affection for Bob Dylan when they made Santos a Dylan fan. But it is the unintentional similarities that make the DVDs of the sixth and seventh seasons, which at the time received mixed reviews, so rewarding to watch now. In both “The West Wing” and in real life, for example, the Phillies played in the World Series during the election campaign.

Image Jimmy Smits, left, as the Democratic presidential nominee, debating Alan Alda, as his Republican opponent, in the final season of the NBC series The West Wing. Credit... Mitchell Haddad/NBC Universal

As the primaries unfolded this year, “I saw the similarities right away,” said Lawrence O’Donnell, a producer and writer for the series who has appeared on MSNBC as a political analyst. Mr. O’Donnell had used Mr. McCain as one of the templates for the Vinick character in the episodes he wrote, though he said that “McCain’s resemblance to the Vinick character was much stronger in 2000 than in 2008.”

Echoing the criticism Mr. McCain faced during the primaries, a White House aide in “The West Wing” contends that Vinick is “not conservative enough” for the Republican base. Sometimes the two candidates’ situations are almost identical: when the press starts asking where Vinick attends church, he tells his staff that “I haven’t gone to church for a while.” Asked in July by The New York Times about the frequency of his church attendance, Mr. McCain said, “Not as often as I should.”

Mr. Alda and Mr. McCain are the same age. When a hard-edged strategist played by Janeane Garofalo joins the Santos campaign, she immediately alludes to Vinick’s age. “He’s been in the Senate for like 90 years. He was practically born in a committee room,” she says.

In the same way that Obama surrogates have subtly knocked Mr. McCain’s lack of computer skills, the Garofalo character remarks to the Santos campaign manager, Josh Lyman: “Why are you always talking about high-tech jobs? Because Vinick uses a manual typewriter.”

Conversely, Santos staffers talk about getting video of the candidate with his “adorable young children hugging their hale and vital dad.” The casting of Mr. Smits introduced story lines about the prospect of a minority president. But when an aide suggests a fund-raising drive in a Latino community, Santos snaps: “I don’t want to just be the brown candidate. I want to be the American candidate.” The Obama campaign has made similar assertions.