The story begins with a family leaving the city through a long tunnel to go on a vacation. There is anticipation that slowly gives way to anxiety as they are in the tunnel. We ultimately learn about what the tunnel does: it closes off, trapping the cars within, who will perish - a kind of population control measure.
This is "The Tunnel Ahead", by Alice Glaser, which can be read in the November 1961 edition of Fantasy & Science Fiction.
A summary from Alice Glaser's entry in The Encyclopedia of Science Fiction:
(1929-1970) US writer and editor, a Radcliffe graduate and social activist who lived in Paris for several years before returning to New York to become an associate editor of Esquire magazine (see Slicks). Her one sf story is the frequently anthologized "The Tunnel Ahead" (November 1961 F&SF), reminiscent in some ways of Shirley Jackson's "The Lottery" (26 June 1948 The New Yorker). In a overcrowded, Dystopian future when the US population has reached one billion, a family returning to Manhattan (see New York) from the crowded beaches must drive through an 8500 foot tunnel – the only way into or out of the city. At random intervals some ten times per week, the tunnel is sealed off and the occupants of the 700-odd trapped vehicles are gassed to help reduce Overpopulation; nevertheless this risk offers city-dwellers their only excitement in life. Glaser also contributed nonfiction to Esquire, but published no other fiction. A short film adaptation of "The Tunnel Ahead" directed by André Øvredal, who made Trollhunter (2010), is in post-production in Norway.
It was the answer to 60s short story, robot cars travel through a tunnel, occupants are liquefied and Looking for story about population control via beach vacation, and accepted for the latter one.