[Hillary Clinton and Donald Trump election 2016 illustration]Mike Nudelman/Business Insider Hillary Clinton is starting off the general election with a healthy lead over Donald Trump, according to a new poll released by the Harvard University Center for American Political Studies and the National Research Group. The survey found that Clinton held a 6-point lead over Trump nationwide and a 4-point lead in swing states. But Mark Penn, one of the pollsters involved in the survey who also served as Clinton's chief strategist during the 2008 presidential campaign, said the results showed she will have to overcome brutal attacks from the mogul with a message that brings together an anti-Trump coalition. "She's got a significant lead, but the country is divided," Penn, a longtime aide to both Hillary and former President Bill Clinton, told Business Insider. He added that Clinton should be reaching across the a "divided" Republican Party while batting aside Trump's onslaught of attacks. Clinton has spent the first week since Trump assumed the position of the Republican Party's presumptive nominee deflecting attacks from Trump that have largely been aimed at her husband's past infidelities. Trump has repeatedly referred to Hillary Clinton as a "total enabler." Clinton has also made a point of taking advantage of the Republican infighting over Trump as the party's presidential candidate. Her campaign has pushed out emails to reporters almost every time a prominent Republican has distanced himself or herself from Trump. The campaign also cut a video quoting Jeb Bush, Lindsey Graham, Ted Cruz, and Marco Rubio — Trump's former presidential rivals — saying negative things about the business mogul. [Hillary Clinton]Mike Nudelman/Business Insider But the poll found that Trump and Clinton are viewed unfavorably by a similar number of voters. The bombastic real-estate magnate's unfavorability rating stood at 60%, while the former secretary of state lagged just behind at 52%. "I think on the one hand the poll suggests you have to worry about those attacks [on Clinton] catching traction," Penn said. "But on the other hand ... if she can begin to generate more enthusiasm to a broader group than the primary, it shows that she goes into this with a significant edge." A part of that coalition-building will have to include supporters of Bernie Sanders, a Vermont senator who remains locked in an increasingly divisive primary battle with Clinton. The poll, which was conducted at the end of March, found that just 64% of Sanders supporters would vote for Clinton in the general election. "Yeah, I mean, I would think that's a little low," Penn said. "It shows again the work she's got to do to bring everyone together. I think she'd want to see that more in the 85% range." Whether Clinton will be able to hit that 85% mark will depend on a number of factors, Penn said — including how Sanders handles the remainder of the race and if he "comes around and endorses her and urges his supporters." "I think, given when Sanders concedes the race and pulls out, the Democratic Party will have find it much easier to consolidate," Penn said. [Donald Trump]Mike Nudelman/Business Insider A factor playing into Clinton's hand, the poll found, is that she's much more trusted than Trump on the top issue: The economy and jobs. Clinton held a 47% to 32% edge for voters who care most about the economy. And that was also before Trump made a series of mishaps while discussing the national debt and economic policy in recent interviews. "She can champion that issue in the face of interviews by Trump that, by themselves would cause huge headaches and gyrations in the financial marketplace community," Penn said. "I think this is off to a good start that way, and I do think that that's absolutely critical for her." Between his comments on the economy and the infighting within his own party, Trump has only helped Clinton since he became the presumptive nominee last week, Penn said. "Usually, becoming the presumptive nominee would give people a lift," he said. "In this case, I'm not so sure he's had a single good day since he's become the presumptive nominee. I think he might have been better off while he was in the [primary] fight." NOW WATCH: FORMER GREEK FINANCE MINISTER: Why Hillary Clinton is a 'dangerous person'