The CNN/Opinion Research survey found 58 percent of those polled do not like the Republican proposal, while 35 percent support it. The plan put forward by Rep. Paul Ryan, R-Wis., would shift Medicare to a system of vouchers for private health insurance although it would not affect anyone who turns 65 in the next decade.
CNN Polling Director Keating Holland said opposition to the Ryan plan cuts across party and demographic lines, with 54 percent of self-described conservatives saying they do not like it.
The poll also found more than half of U.S. residents believe the Republicans should cooperate more with President Barack Obama.
Immediately after the November 2010 election, when the Republicans won control of the House, a CNN poll found more than half the public, 52, percent, was pleased by the results while 39 percent were not. That has now dropped to 48 percent please and 44 percent not pleased.
"The results of those two questions, taken together, suggest that in the 2010 election voters wanted to give the GOP enough power to act as a check on the Democrats, but did not vote to give the GOP a mandate to enact its entire agenda," Holland said.
Opinion Research polled 1,007 U.S. adults by telephone May 24-26. The margin of error is 3 percentage points.