WASHINGTON

In March 2010, on the day before President Obama was to sign the Affordable Care Act into law, a group of senior Republican aides huddled in Senator Mitch McConnell’s Capitol suite to try to come up with a catchy slogan to use against it.

Many conservatives were simply advocating a vow to repeal the new law, but Republican strategists worried that pressing for repeal without an alternative could backfire. So they batted around a few ideas before Josh Holmes, then a top communications adviser to Mr. McConnell, tossed out the nicely alliterative phrase “repeal and replace.” That seemed to do the job, with its promise to get rid of the new law detested by Republicans while suggesting that something better would follow.

The phrase has shown real staying power: President-elect Donald J. Trump proudly invoked “repeal and replace” twice during his news conference on Wednesday.

“The goal was to come up with something that had durability and could be a rallying cry for Republicans basically to campaign against Obamacare,” said Mr. Holmes, now the president of Cavalry, a consulting and media firm. “This obviously had sort of a catchy ring to it. And it was consistent with what we were trying to accomplish.”