MILWAUKEE — President Obama said on Thursday that enrollment in health coverage under the Affordable Care Act had reached a new high, 20 million, and he called the law an overwhelming success in this city and around the nation despite Republicans’ implacable opposition.

“Congressional Republicans have tried and failed to repeal Obamacare about 60 times,” Mr. Obama said to an audience here. “They have told you what they would replace it with about zero times.”

He continued, his voice rising: “If they got their way, 20 million people would have their insurance taken away from them. Twenty million people!”

The 20 million figure includes people who have received private health insurance on exchanges, those who gained Medicaid coverage under state expansions and young adults who were able to stay on their parents’ health plans until age 26, the administration said.