The phrase 'deep swig' is correct and usable in written English.
You can use it to refer to someone taking a long, deep sip from a drink. For example: She took a deep swig of her iced latte and let out a content sigh.
"Why wouldn't a new owner want the cross?" "Well," I said, taking a deep swig of my frosty see-through, "they might be, I don't know, Jewish, or whatever.
A guy in a white vest and tabletop hair takes a deep swig from a two-pint glass of water, as his buddy and a few stray cops help clear a block-long path, shooing tipsy groups hugging yard glasses of blue liquid out of the way.
A Nashville journeyman with a taste for classic 1960s soul, Anderson East takes his deepest swig yet of that genre with his new album, "Encore". Blink and you might think you're listening to an above-average Otis Redding impersonator, or Joe Cocker's long-lost nephew.
At this point, those who have taken a deep, greedy swig of the nonsense Mitt Romney is pouring all over the media this election cycle might have an 'A-ha!
"They called her the Mother of the Blues," Ms. Braden says with a deep chuckle and a swig of gin.
The Harry Potter star pauses, bites his lip and, deep in concentration, takes a swig of Coke.
Occasionally, some reporter on deadline would snap his fingers and, between deep puffs of his cigarette or a swig from his whiskey flask, ask me to get a factoid for his story.
An impulse pulling at something deep within me, something strong, tells me to swig it down, all mixed with seawater and sailor spit.
So deep was his state of denial that he was swigging chablis at the time.
He begins irresistible, holding court for Rose and best friend Bono Stephen Hendersonn) in the backyard, a few swigs of gin down – ebullient and mesmeric, deep sweetness cancelling out that hint of bitter.
The best examples are bright and hoppy up front but finish short, like taking a deep whiff of a fresh-cut grapefruit and then a swig of Topochico.
