Story highlights Hillary Clinton leads Donald Trump, 49% to 37%, in a new national poll

A narrow majority of voters say Trump could best handle shootings like the Orlando massacre

Washington (CNN) Hillary Clinton has a 12-point lead over Donald Trump nationally, a new Bloomberg Politics poll shows.

Clinton has 49% support to Trump's 37%, with Libertarian Gary Johnson at 9%, according to the poll of 750 likely voters. The poll was conducted Friday through Monday and released Tuesday evening, meaning many of those polled were surveyed before the Orlando terrorist attack.

Particularly damaging for Trump: 55% of those surveyed said they would never vote for him, compared to 43% who said they'd never back Clinton.

It's a much larger lead than Clinton held in national polls conducted in May and early June, prior to Trump's accusation that the federal judge in the Trump University lawsuit is biased because his parents were born in Mexico and Trump is advocating a U.S.-Mexico border wall.

The poll also asked voters to what degree recent Trump and Clinton controversies "bother" them.

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