There's no evidence that's true.
During a news conference today, Spicer clarified that his assertion extended beyond just the in-person audience.
Even including TV watchers, Trump trailed several prior presidents. He falls into fifth place since 1969, behind Obama in 2009, Richard Nixon in 1973, Jimmy Carter in 1977 and the high-water mark of Ronald Reagan in 1981.
The New York Times spoke to crowd estimation experts who pegged the number in attendance on Saturday at one-third of Obama's 2009 audience, or 600,000 people. Other attendance figures are from the Atlanta Journal-Constitution. Nielsen numbers were reported by Variety.
On top of television, Spicer added online streaming numbers in his news conference today. He cited CNN's number of streams, which the network pegged at 16.9 million. Add that to Trump's Nielsen numbers, Spicer suggested - 30.6 million - and you're already past Reagan and everyone in the pre-Internet era.
That 16.9 million number, though, was streaming starts, meaning that someone popped into the stream and then left it. The maximum number of concurrent viewers - a more comparable number to Nielsen metrics - was 2.3 million at the time Trump took the oath. That would put Trump still 6 million views behind Obama in 2009 and far behind Reagan.
Spicer's argument also ignores that, eight years ago, CNN's livestream numbers for Obama were even bigger. As AP reported at the time, CNN had 21.3 million streams (presumably starts) in partnership with Facebook that year. The AP had 8 million and the White House itself 1.3 million.
There were certainly more places streaming the event on Saturday than in years past, including on any number of media websites and on Twitter. One analysis of Twitter viewership found that the inauguration was less popular than other recent events, including election night.
It's clear that Trump's assertion that 1 million to 1.5 million people attended his inauguration is without merit. Spicer pointed out on Sunday that there are no official counts of attendance from the National Park Service, highlighting that any such estimates are necessarily murky.
Then Spicer tried to flip similar murkiness to his advantage, retrofitting Trump's original claim about record-setting into being accurate on a different metric: Total global viewership.
He pointed to unrepresentative streaming numbers to bolster that case and took advantage of the lack of a unified measurement system for online video to make a prove-me-wrong argument. Numbers are too murky to know that Trump was wrong about how many showed up and they're too murky to know that Trump didn't set a new global/online record.
Excluding online streaming, Trump starts out 8.3 million views behind Obama in 2009. It seems hard to believe that Trump's audience - which skews older than Obama's did at that point - preferred to watch on Twitter than to watch on CNN.
There was one new audience that could possibly have helped shift the numbers. That analysis of Twitter's stream found that viewership in Russia doubled compared to election night, and, apparently for the first time, it ran on Russian state TV. It's not clear, though, how many tuned in.
Maybe Russia propelled Trump to an unexpected victory. The only problem for Spicer's claim is that there's no evidence that it did.