Broxton, who entered the game after starting right fielder Michael Conforto suffered a concussion, had the chance to play the role of hero. The Mets had already scored two runs off Nats closer Sean Doolittle as part of their ninth-inning rally.
Instead, the 29-year-old Florida native struck out as the Mets dropped to 20-22 with their second straight loss.
"From the start of the season, I've been surprised at why I haven't been playing as much and why I haven't got as many opportunities," Broxton told reporters after the game. "It's not like I started out bad. It's just, it is what it is."
The Mets announced Friday he'd been designated for assignment. The front office has seven days to trade him or place him on irrevocable waivers. If he clears waivers, he can be released or sent to the minor leagues.
Broxton posted a .143/.208/.163 slash line with no home runs and four stolen bases across 34 appearances for the Mets after being acquired in a January trade with the Milwaukee Brewers.