Republicans were also much less likely than Democrats to think Russian Federation influenced the 2016 presidential election, with only 9 percent of Republicans compared with 75 percent of Democrats taking that view.
Just before Trump's inauguration in January, 50% of voters said the United States was a more divided nation after eight years of the Obama presidency, but Republicans and unaffiliated voters felt that way much more strongly than Democrats did.
The poll conducted by the Associated Press was done before the shooting incident at a baseball field on Wednesday, June 14, which left a congressman injured.
While that sentiment appeared most common among Democrats and independents - 9 in 10 and 6 in 10, respectively - a third of Republican voters said Trump had little or no respect for democratic institutions in America.
Trump was unpopular among Americans overall even as he was elected president, but the poll shows that even many Republicans have doubts.
Special counsel Robert Mueller has also been appointed to oversee the Russian Federation investigation.
Bernie Sanders Ally Tom Perriello Loses Virginia Gubernatorial Primary to Ralph Northam
The lieutenant governor is a part-time position that involves presiding over the state Senate and breaking tied votes. Both support a higher minimum wage, free community college, decriminalizing marijuana and expanded pre-K.
"The rumblings that Ted Cruz was damaged by his presidential campaign were overstated", said Jim Henson, head of the Texas Politics Project at the University of Texas at Austin and co-director of the poll.
When asked about Russia's impact on the 2016 election, only 8 percent of Republicans thought interference influenced the outcome, and only 9 percent of the same group thought that the Trump campaign and Russian Federation colluded in an effort to affect the campaign. For example, as long as Trump maintains 80 percent job approval among Texas Republicans, it is inconceivable that Republicans in the Texas congressional delegation will entertain any idea of impeachment proceedings.
Sixty-three percent disapprove of Trump's handling of foreign policy, 60 percent disapprove of his handling of immigration, and 55 percent disapprove of how he's handling the economy.
Seventy-five percent of Americans disapprove of the job Congress is doing, the poll shows.
Results for this Gallup poll are based on telephone interviews conducted June 7-11 with a random sample of 1,009 adults, aged 18 and older, living in all 50 USA states and the District of Columbia.
Respondents were first selected randomly using address-based sampling methods, and later interviewed online or by phone.
The University of Texas/Texas Tribune internet survey of 1,200 registered voters was conducted from June 2 to June 11 and has an overall margin of error of +/- 2.83 percentage points.