Roughly 50 percent of Democrats and 59 percent of Republicans surveyed say the GOP takes the cake when it comes to effective messaging about the president's signature health reform law.

The survey, conducted Sept. 30 through Oct. 2, polled 89 Democrats and 100 Republican Political Insiders. When the Affordable Care Act exchanges opened for enrollment on Oct. 1, consumers faced website glitches which prevented some from signing up for insurance.

"The glitches, flaws and implementation delays all contribute to the GOP effort," noted a Republican responder.

However, not all agreed that the GOP efforts have been successful. A small group of responders—25 percent of Democrats and 12 percent of Republicans—thought the Democrats have been more effective in their Obamacare messaging, with some attributing the Republican failure to the right-most contingent of the party.

"We're living in an echo chamber while Obama is aiming for middle-of-the-road voters who hate Congress even more than they dislike Obamacare," wrote a Republican responder.

But 25 percent of Democrats and 29 percent of Republicans said neither party has done a good job.

"Democrats have failed to explain what it is and why people should care," wrote a Republican responder. "Republicans have failed to offer an alternative. F grades to both."

See full poll results here.