The president's approval rating, which has proved historically bad since he took office, has sunk again.
The only government official who scored higher than Trump in Zogby's poll was Trump's Secretary of Defense James Mattis, who scored an approval rating of 43 percent. His disapproval rating, meanwhile, has jumped to 57%.
But even general support for Mr Trump among his party has dwindled, from 83 per cent in April to 72 per cent in June.
In Rasmussen's survey conducted June 13, which included 1,500 likely US voters and a margin of error of 3 percentage points, only 43 percent of likely voters approved of Trump's presidency.
Polls closed in race for Mulvaney's replacement
Republican Ralph Norman and Democrat Archie Parnell are competing for Mick Mulvaney's seat in South Carolina's District 5. South Carolina's 5th District has been held solidly by Mulvaney since his 2010 victory.
When asked about the objective of the investigations, 32 percent believe it is a political distraction that should be put aside, 27 percent said it's serious but not as serious as other issues and 39 percent called it a critical issue of national security. Twenty-seven percent thought it was a serious issue but not as serious as other issues.
The CBS poll was of 1,117 adults nationwide and was conducted between June 15 and June 18.
The latest poll has a margin of error of 4 percentage points.
Other recent surveys haven't brought good news for Trump either.
Polls showing the president this close to a majority approval rating are impossible to come by because they don't exist, so it's no surprise that the insecure Trump would lean on an outlier survey from a Republican-leaning pollster.
When CBS last polled Trump's job approval rating in late April, his approval rating was 41%.
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