But there's one group watching her GOP outreach with wary eyes: her progressive supporters.
One of Clinton's persistent criticisms from the left has been that her foreign policy is too conservative.
Vermont Sen. Bernie Sanders hit Clinton throughout the primary for her vote in favor of the Iraq War and past support of free trade deals. And the liberal blogosphere has long labeled Clinton part of the neoconservative wing, a conservative intellectual movement that supports an interventionist foreign policy.
Clinton has welcomed Republicans' support without making policy outreach. Her campaign has reached out to big Republican names for endorsements and one of them, Hewlett-Packard CEO Meg Whitman, is even hitting the campaign trail for Clinton. Also in Clinton's camp are Brookings Institution scholar and former Republican adviser Robert Kagan, foreign policy presidential adviser Brent Scowcroft, former Bush administration official Richard Armitage and former Bush Treasury Secretary Hank Paulson.
Even Paul Wolfowitz, the former George W. Bush administration official credited as one of the architects behind the Iraq War and an anchor of the neocon movement, said he may vote for Clinton.
Green Party presidential candidate Jill Stein, who has the most to gain from a liberal defection away from Clinton, pointed to the Democratic candidate's GOP support in an interview
with The Washington Post this month as a sign of Democrats resembling the GOP.
"You can also look at Hillary's new organization for reaching out to Republicans. The massive influx of Republicans into her campaign... it reflects what her agenda is," Stein said.
Later she tweeted
: "Iraq War mastermind Paul Wolfowitz plans to vote Clinton: latest example of the Dems becoming neocon war hawks' preferred party. #NoMoreWar."
For now, Clinton's hold on self-identified Democrats remains strong, while Trump has a higher than normal defection rate of Republicans. Progressives that lined up behind her campaign after Sanders was eliminated from contention aren't scared off -- yet.
Still, those liberals will be closely watching the presidential debates to see how far Clinton's recruitment of Republicans goes, said Symone Sanders, Bernie Sanders' former press secretary.
"As long as Secretary Clinton doesn't move on the issues or promises she has made to her supporters, that she has made to the progressive movement, as long as she upholds the most progressive platform in party history... she's in safe territory," Symone Sanders said. "But the moment these progressives feel these endorsements influence where she stands on the issues, that becomes a problem and that's where she loses that support."
Asked about her name-dropping prominent GOP politicians in a recent speech attacking Trump's rhetoric on race and whether that was an overture to Republican voters, Clinton said she is "absolutely ... reaching out to everyone."
"This is not a normal choice between a Republican and a Democrat ... we are facing a divisive candidate who's loose-cannon temperament and his complete lack of preparation make him unqualified to be president," she told MSNBC's "Morning Joe" last week. "I am reaching out and asking fair-minded Americans to repudiate this kind of divisive demagoguery."
Pollsters say there doesn't appear to be a movement of "Clinton Republicans" the way "Reagan Democrats" reshaped American politics.
"Obviously, these defections are creating a real problem electorally for Mr. Trump," said Peter Brown, assistant director of the Quinnipiac University poll. "Compared to four years ago, twice as many Republicans say they're going to vote for the Democratic candidate than did so four years ago. ... But to try to make this into a movement that has multi-election legs, we don't know."
Brown noted that what has been historic about this election is the unprecedented high unfavorability ratings of both candidates. Monmouth University pollster Patrick Murray echoed Brown, saying that a majority of voters are voting against a candidate rather than for someone.
"These are not Hillary Republicans, these are anti-Trump Republicans," Murray said. "And I don't see anything Hillary Clinton's doing that is specifically designed to appeal to Republicans in terms of a vision that is designed to appeal to a specific segment, which is what Reagan did."
Both pollsters also said their data shows few warning signs for Clinton with progressives at this point. Murray said many of Sanders' die-hard supporters were never reliable Democratic voters, and thus haven't impacted Clinton's base as they've gone back to their independent tendencies. But if the race tightens, she could use that support.
Former adviser to President Barack Obama and Democratic strategist David Axelrod, called the phenomenon more "Trump Democrats" than "Hillary Republicans," and said that as long as Clinton's opponent is Trump, she has some leeway with progressives.
"The severity of the threat that many Democrats and some Republicans think that Trump represents gives her a lot of running room," said Axelrod, a CNN commentator.
That's the viewpoint of some of the Republicans endorsing Clinton, as well. Former Bush official Ricardo Reyes co-founded the group R4C (Republicans for Clinton) to make the case that Republicans should vote for Clinton over Trump, but vote for the GOP down the rest of the ticket.
He said he and his supporters had hoped for an alternative to Trump within the party or from a third-party candidacy, but that didn't emerge.
"When (RNC Chairman) Reince Priebus and (House Speaker) Paul Ryan said it was a "binary choice between Trump and Clinton, and that made it very, very stark for us," Reyes said, adding Clinton has a history of bipartisan work in the Senate. "Do I agree with Hillary Clinton and all her policies? Of course not. I don't think Democrats do either. But if you step back and you think one candidate is going to careen this country into oblivion, and you have another candidate who has a history of working with others, then it's clear."