As Mrs. Clinton prepares to accept the Democratic Party’s nomination at the convention in Philadelphia this month, she will confront an electorate in which 67 percent of voters say she is not honest and trustworthy. That number is up five percentage points from a CBS News poll conducted last month, before the F.B.I. released its findings.

Mrs. Clinton’s six-percentage-point lead over the presumptive Republican nominee, Donald J. Trump, in a CBS News poll last month has evaporated. The two candidates are now tied in a general election matchup, the new poll indicates, with each receiving the support of 40 percent of voters.

Mr. Trump is also distrusted by a large number of voters — 62 percent — but that number has stayed constant despite increased scrutiny on his business record and falsehoods in his public statements and Twitter messages.