The designation provides Ms. Abrams, 45, with a nationally televised platform to burnish her profile at a time when she is said to be considering her next political steps, including a possible run for Senate in 2020 against Senator David Perdue, Republican of Georgia. But it also carries substantial risks: A notoriously awkward format, State of the Union responses have been more memorable in recent years for the memes they have produced than persuasive oratory.

They have damaged rising stars of the past. Bobby Jindal was widely panned in 2009 when, as governor of Louisiana, he delivered the Republican response to Barack Obama’s joint address to Congress, and Senator Marco Rubio’s response in 2013 is remembered more for his sudden lunge for water than his answer to Mr. Obama.

The buildup to this year’s address has been more dramatic than past years. Speaker Nancy Pelosi originally invited Mr. Trump to deliver the annual address to Congress in the House chamber this week, but she rescinded that invitation amid the government shutdown. On Monday, with the government reopen, the speaker and the president agreed to a new date, Feb. 5.

Mr. Schumer alternates with Ms. Pelosi each year on choosing the Democratic respondent. Last year, Ms. Pelosi selected Representative Joseph P. Kennedy III of Massachusetts, the scion of a Democratic dynasty who is among the party’s most popular young figures. Without using Mr. Trump’s name, Mr. Kennedy chastised the Trump administration for “a rebuke of our highest American ideal” and pledged to fight for the millions of immigrants brought to the country illegally as children, known as Dreamers.

In 2017, Mr. Schumer chose Steve Beshear, the former governor of Kentucky, to deliver a response to Mr. Trump’s first joint address to Congress.