WASHINGTON—The one-year anniversary of President Donald Trump’s inauguration didn’t quite unfold according to script.

Unable to prevent the first federal government shutdown in more than four years, Mr. Trump chose to remain in Washington on Saturday. He had to bail on his own party at his Palm Beach resort, where Republicans gathered to commemorate the inaugural anniversary. There was no golfing for the president in South Florida’s 70-degree weather, as is traditional during his visits.

While Mr. Trump stayed home, the fundraiser went off as planned. Most of the roughly 100 people who paid up to $250,000 for a ticket were still expected to attend, according to people familiar with the plans.

Mr. Trump’s son Eric and daughter-in-law Lara Trump were set to host the event with Republican National Committee Chairwoman Ronna Romney McDaniel as the guest of honor.

The president, who spent much of the day upstairs in the White House residence, sent a videotaped message instead of rubbing shoulders with supporters at his Mar-a-Lago property.