The Biden campaign was hardly shocked by the Times/Siena poll.

The sour numbers for President Biden in the new polls of battleground states from The New York Times and Siena College did not come as a surprise to officials in his re-election campaign.

The campaign’s internal polling had in recent weeks found Mr. Biden losing ground among voters of color, a key Democratic Party constituency, and trailing former President Donald J. Trump in important battleground states.

On Sunday, the Biden campaign circulated talking points to its surrogates that downplayed the relevance of polling in general, questioned how much voters are tuned into the 2024 contest a year away from Election Day and offered a reminder that past presidents have had lousy approval numbers before being re-elected.

“Our campaign is being built to win an election in November 2024 — not the next New York Times poll,” said Kevin Munoz, a Biden campaign spokesman.

Biden aides pointed to a clip of Donna Brazile, the veteran Democratic operative, delivering an authorized don’t-fret message during a Sunday morning appearance on the ABC program “This Week.”

“I’m old enough to remember that Ronald Reagan was trailing in 1980 for his re-election,” Ms. Brazile said. “I’m old enough to remember when Bill Clinton was trailing, and Barack Obama was toast right before the 2012 re-election. Don’t count out Joe Biden.”