(CNN) Most Americans continue to believe that the Russian effort to influence the 2016 presidential election is a serious matter that should be investigated, but the constant criticism by President Donald Trump of special counsel Robert Mueller is taking its toll, according to a CNN poll conducted by SSRS released Friday.

The number of Americans who approve of how Mueller is handling the investigation has dropped from 48% in March to 44% in May to just 41% now, the lowest it has been in CNN's polling. Mueller has a lot of company; no one connected with this matter is coming out of it in a positive light. Mueller's favorable rating is just 32%; former FBI director James Comey's favorability is just 28%; Rudy Giuliani, one of Trump's lawyers in the Russia investigation, is viewed favorably by only 31% of Americans.

And look how Giuliani's public image has really taken a hit. Once upon a time, America's Mayor was viewed favorably by two-thirds of all Americans. As recently as 2011, a majority still had a positive view of him. In 2016, his favorable rating was 19 points higher than his unfavorables. Now 45% have an unfavorable view of Giuliani and only 31% see him in a positive light.

Negative views of Mueller don't mean that the public is taking Trump's side. Just 29% approve of how Trump is handling the Russia investigation. Only 35% say it is an attempt to discredit Trump's presidency. Nearly 7-in-10 think Trump should testify under oath if Mueller requests it. Another 70% would disapprove if Trump issues himself a presidential pardon, with no majority in any demographic group. Trump has said he absolutely has the power to pardon himself but doesn't need to.

Russian President Vladimir Putin is doing poorly among Americans but no worse than usual. While his favorability ratings are extremely low (11% favorable, 72% unfavorable), they've been that way for a while.

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