With millions of consumers getting cancellation notices for their current health plans, President Obama announced Thursday that he will encourage insurance companies to continue offering their customers the same health plans next year.

“This fix won’t solve every problem for every person,” Obama said, saying he would consider legislative action to go further. But he appeared to rule out the sort of legislation that House Republicans are pushing, which would allow insurance companies to continue selling new policies, indefinitely, that would not comply with the law’s new consumer standards.

“I will not accept” legislation that would “drag us back to a broken system,” Obama said.