Results of the CNN/ORC International survey released Monday indicate 54 percent think it's a bad thing that the GOP controls the House, up 11 points from December, while 38 percent say it's a good thing the GOP controls the House, a 13-point drop from December.
CNN said it is the first since Republicans took back control of the House in 2010 that a majority say their control of the chamber is bad for the country.
Results also indicated that 30 percent of the public said Boehner, who became speaker in January 2011, should keep his role while 63 percent said he should leave his post.
The survey also indicated the approval rating for Congress remains near an all-time low. Only 12 percent of those questioned say they approve of the job Congress is doing while 86 percent expressed disapproval of lawmakers.
Forty-four percent say they approve of the job the president is doing with 52 percent saying they disapprove, CNN said.
Results are based on a national telephone survey of 841 adults conducted Friday through Sunday. The margin of error is 3.5 percentage points.