Trump, perhaps sensing a pattern, asked the infant if he wanted to go back to his mommy and daddy or stay with Donald Trump.
In an NBC/WSJ poll released Monday, Clinton has a double-digit lead against Trump, garnering 46 percent of voters' support to Trump's 35 percent.
Several people dismissed Trump's comments - which included grabbing women by the "pussy" and letting him kiss them because he's a star - as immature but perfectly typical.
He also talked about Clinton's deleted emails, and the audience chanted "Lock her up!"
Trump made waves at the second presidential debate when he said that if he becomes president, he'd seek to imprison Clinton over her email controversy - a stunning departure from the typical decorum of American politics.
She also said she was satisfied with how he handled the aftermath of the leaked recording.
TRUMP: We have an absolute incredible situation taking place, folks, and I will never stop fighting for you against the Washington establishment that has betrayed each and every one of you.
Trump apologized shortly after the release and to some Northeastern Pennsylvania supporters, including women, it was good enough. "What you get from Donald Trump is edgy, but it's real". "I may be limping across that finish line, but we're going to get across", a rueful Trump said on Monday.
Some supporters said their faith in Trump's chances was unshakable, even amid his drop in the polls over the last two weeks and the chaos within the Republican Party.
The crowd then erupted with cheers, and Trump handed the boy back to his parents.
"I have had the experience of going into a crowd and someone has their hand inside my shirt", she said. "I don't know where we're going as a country".
"Who cares?" Anna DeAngelo, 44, of Scranton, said.
Trump's Virginia chairman, Corey Stewart, who helped organize the RNC protest, said Ryan and other party elite didn't understand that "the grass roots took control of this party when we nominated Donald Trump".
The national conversation about sexual assault is "a powerful thing", said Delilah Rumburg, CEO of the National Sexual Violence Resource Center in Harrisburg, Pennsylvania.
Forty Republican senators and congressmen have revoked their support for the Republican presidential nominee - with almost 30 of them calling on him to quit the race altogether in recent days.