But the party seems adrift and divided for now over how to reshape it to attract enough votes to muscle it through the chamber.
White House officials and leading legislators plan to resume talks today.
They huddled for two hours in a Capitol basement meeting room. But they failed to cut a deal on a White House proposal to let states seek federal permission to drop coverage mandates that President Barack Obama's health care law slapped on insurers.
The White House offers got an uneven reception earlier from GOP moderates and conservatives. That dimmed prospects they could salvage one of their leading legislative priorities.