For Ms. Stefanik, 35, once the youngest woman ever elected to Congress, the moment in the spotlight was noticed by members of her party, most notably President Trump, who called her a “new Republican star” on Twitter.

But her performance was also a galvanizing moment for Democrats, who swarmed Ms. Stefanik’s Democratic challenger, Tedra Cobb, with social media attention and donations: Ms. Cobb’s campaign announced a weekend fund-raising haul of more than $1 million.

Among the wave of donors was George T. Conway III, a conservative lawyer who is married to President Trump’s White House counselor, Kellyanne Conway, and is now a prominent critic of Mr. Trump. Mr. Conway posted a screenshot of his $2,800 contribution on Twitter, and was among other left-leaning social media luminaries, including Chrissy Teigen, George Takei, Mark Hamill and Zach Braff, who encouraged their followers to follow suit.