Checkmate by Edward Wellen from Isaac Asimov's Science Fiction Magazine, December 1980; it's on the Internet Archive here.
Searching for the last man on Earth:
She walked out onto the floor. The vast maze of the production line was almost entirely automated. She spotted just three workers among the rolling pills and marching bottles. Down among the capping and sealing machines she braced the first.
The sister popped her gum thoughtfully. "Vernon Gardner? Ain’t that the name of the guy that’s still alive? What would he be doing here? Hell no, I ain’t seen him.”
"I heard he worked here once — Before.”
"Well, he don’t work here now. Believe you me, I would’ve noticed him.”
She thinks it might be a guy she once knew and that she told him that she would only date him if he was the last man alive.
When Vernon ventured to inform her that he loved her, something she took for granted, and when he compounded that by propositioning her, she did not say, "Get lost, you creep.” But that was the burden of her response. Because she did say, could not resist saying, "Maybe if you were the last man on earth ...”
Disease:
The commemorators had hardly scattered to their homes when Checkmate struck.
"Checkmate,” some headline-writer called the plague, and the name stuck. The disease spread with Concorde speed. It was no localized Egyptian plague. It left no spot on Earth untouched. Human males of all ages, climes, and persuasions dropped like sprayed flies.
And turnabout:
He was mad, of course, but gloriously mad. No, it was not all madness. Above all, it was love. If that was madness she was mad too.
"You did it all for me?” She wanted to hear him say it.
And he did. Readily. "Of course it’s all because of you, Bonnie.”
"Then take me.”
Almost at once emptiness filled her.
Vernon gazed through her as though seeing all the world’s lonely lovely women.
"Things have changed, Bonnie.”
She stood stunned, her head in a roar.
Slowly he focused on her and gave her a half smile.
"Maybe if you were the last woman in the world. . . .”"Maybe if you were the last woman in the world. . . .”
After the shock of that passed, Bonnie looked thoughtful.After the shock of that passed, Bonnie looked thoughtful.