More than one-third of the respondents said Trump's treatment of the investigation lowered their opinion of him.
Americans also believe that he's been criticized more than recent presidents.
CBS found that the most popular reason people cited for their disapproval was Trump's potential ties to Russian Federation. Most who approve of the President say it is not serious.
A CBS News poll shows the president's approval rating is down to 36 percent, 57 percent of Americans polled disapprove of the job he's doing.
CBS News' report added that over recent presidents have seen their support reach similar levels with their party's voters, which is true.
Gergen: Trump could beat Dems in 2020
Back in 2001 Hoyer and Pelosi faced each other for the top leadership position inside the Democratic caucus, but have largely worked collaboratively in the top two slots for years.
The June 18, 2010 Rasmussen poll - taken at the same point in Obama's first term - showed the former president with an approval rating of 41 percent compared to a disapproval rating of 58 percent.
The president claimed his critics are not stopping him from getting on with his promise to "Make America Great Again", when he fired up his Twitter account on Sunday morning.
Republicans approve of how Mr. Trump is handling the Russian Federation issue, but in far lower numbers (at 57 percent) than their support for the job he's doing on the issues of the economy (80 percent) and terrorism (77 percent). Another 27% said the investigation is serious but not as serious as other issues.
Thirty-nine percent said the investigation is a critical natural security issue, although 32% said it is a political distraction. Views among whites with a college degree remain more negative. A vast majority of Americans from both parties - 81 percent - think Trump should not try to stop Special Counsel Robert Mueller's investigation, and 56 percent of respondents said they think the investigation will be impartial.
CBS found Trump's approval ratings have been hurt by his reaction to the multiple investigations of Russian interference in last year's presidential election, which he repeatedly has described as a "witch hunt" and an excuse by Democrats to explain former US secretary of state Hillary Clinton's stunning upset loss to him.
- Gamecocks nominated for Best Team ESPY
- Obama: Senate bill is a tax cut, not health care
- Nitish Kumar's JD-U to support Ram Nath Kovind in Presidential elections
- Authorities charge man in mosque incident
- Apache Corporation (APA) Shares Sold by CIBC World Markets Inc
- North Korea carries out another rocket engine test
- ICC Champions Trophy: Waqar Younis pitches into Eoin Morgan's 'lame excuse'
- Former MPD officer found not guilty in shooting Sylville Smith
- FIFA Confederations Cup: Mexico came from behind to beat New Zealand
- How to watch the 2017 National Basketball Association draft