While the poll shows a majority overall opposed to Trump pulling the plug on the Deputy AG, there are sharp differences by party. Among Republicans, 27% say the President should fire Rosenstein, 39% that he should not, with another 34% saying they're not sure what the President should do. Democrats are firmly anti-firing: 72% say Rosenstein shouldn't be fired vs. 12% who think he should be.

Overall, about six in 10 say the Russia investigation is a serious matter that should be fully investigated, while about a third consider it mainly an effort to discredit Trump's presidency. Those figures have held steady in the last month.

The public's approval ratings for Mueller (48% approve, 36% disapprove) and the President (33% approve, 54% disapprove) have also held roughly even in the last month.

The CNN Poll was conducted by SSRS October 4 through 7 among a random national sample of 1,009 adults reached on landlines or cellphones by a live interviewer. Results for the full sample have a margin of sampling error of plus or minus 3.8 percentage points.