Hillary Clinton has a double-digit lead over Donald Trump in a new national poll released Tuesday.

The survey, from Bloomberg Politics, finds Clinton leading Trump by 12 points (49 percent to 37 percent) among likely voters nationally. Nine percent of likely voters chose Libertarian candidate Gary Johnson.

Many likely voters also had strong views about whether they could support the other candidate in the race. Of those surveyed overall, 55 percent said they could never support Trump; 43 percent said the same of Clinton.

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And in a smaller sample of likely voters taken Monday night, after the mass shooting in Orlando, voters said by a small margin--45 percent to 41 percent--that they'd choose Trump when asked which candidate they'd have more confidence in if a similar attack took place next year.

Overall, voters see Trump as better on combating terrorism: they chose him over Clinton on the issue 50 percent to 45 percent. Still, 61 percent did not agree with Trump when he said President Obama "hasn't taken forceful enough action" to combat terrorism in the U.S.

As for the candidates' proposals for how to prevent future attacks, neither gets a majority. Sixty-nine percent of likely voters disagree that there should be more surveillance of American Muslims; meanwhile, 50 percent said the U.S. shouldn't ban the sale of all semi-automatic weapons.

Sixty-two percent of those surveyed said they are bothered "a lot" by Trump's inflammatory comments about women, and 55 percent said the same about his comments on federal judge Gonzalo Curiel's Mexican heritage. For Clinton, the thing most voters are bothered by are her paid speeches on Wall Street: 50 percent said they are bothered "a lot" by those speeches.

The poll surveyed 1,000 U.S. adults and 750 likely voters from June 10-13. The margin of error for the full sample of adults is +/- 3.1 points, and for the likely voters it's +/- 3.6 points.