A new poll shows support for Obamacare has dropped to an all-time low of 35 percent, with a new record 62 percent opposed.

The CNN/Opinion Research poll last month showed the law had a 40 percent approval rating, with 58 percent opposed.

The poll contrasts with a Washington Post-ABC News poll last week which actually showed support for the law rebounding slightly, to 46 percent, as problems with the HealthCare.gov Web site decreased.

Despite the improvements, though, there remain huge questions about the law's implementation. The Obama administration last week announced another major last-minute change, exempting people with canceled plans from some of the law's requirements.

Of the 62 percent who disapprove of the law, 43 percent do so on the right, while 15 percent say the law isn't liberal enough.