"And the fact is the Republicans biggest fear at this point is not if the ACA will fail, what they are worried about is if it's going to succeed," Obama said.
The president has been ramping up efforts to raise awareness about the law's benefits.
He held a large rally at a Maryland Community College, encouraging students there to take advantage of the open enrollment period that begins October 1.
Some Republicans meanwhile are doing their best to defund the Affordable Care Act.
"The American people don't want the president's health care bill and they don't want the government to shut down. Republicans are listening," House Speaker John Boehner said.
While a looming government shutdown seems less likely next week, the next days could be very contentious.
The Senate has moved ahead on a bill that would temporarily keep the government running, and funding for Obamacare intact, but there are worries that it could be defeated by the House.