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Wiktionary
don't hold your breath

phr. (context idiomatic imperative English) "Don't wait." Said cynically to suggest that what has just been mentioned to is unlikely to happen soon or at all.

Wikipedia
Don't Hold Your Breath

"Don't Hold Your Breath" is a song recorded by American singer Nicole Scherzinger for her debut studio album, Killer Love (2011). It was written by Josh Alexander, Billy Steinberg and Toby Gad and produced by the former two along with Carl Falk, Steve Angello and Rami. The song was released on February 16, 2011, as the album's second single in the United Kingdom. "Don't Hold Your Breath" was critically acclaimed, with critics preferring it over singles by The Pussycat Dolls, as well as praising the empowering message and theme. The pop production was also praised.

The song's lyrics speak of the female protagonist realising that her relationship with her man is over and she is not going to return to what used to be. A demo version of "Don't Hold Your Breath" with lead vocals from Timbaland and Keri Hilson leaked in 2010. Then in early January 2011, a second demo version with an altered production, different lyrics and uncredited female vocals also leaked. This was followed by a third unfinished version, this time with Scherzinger's vocals, before the final version premiered on January 14, 2011.

An accompanying music video for "Don't Hold Your Breath" was directed by Rich Lee, and follows Scherzinger as she experiences the emotions of the song. Scenes include a hackney carriage journey, self-realisation, scornful glances in a mirror and wandering an old 1930s house. It was met with generally positive reviews from critics, who described it as one of Scherzinger's most personal music videos to date.

Scherzinger performed "Don't Hold Your Breath" in a series of live appearances such as a performance on Let's Dance for Comic Relief and Good Morning America. The song has also achieved commercial success by topping charts in Poland and the United Kingdom, as well as reaching the top twenty in many other countries.