One issue where that's a problem: Free trade.
Trump's opposition to U.S. free trade deals isn't just a policy position -- it's an animating issue of his campaign, and a staple of every speech and interview. In fact, to the extent there's an issue Trump has been consistent on during his political life, this is probably it.
Even in Trump's 2016 political launch, while his anti-immigrant position garnered the most attention, he also proclaimed: "Free trade can be wonderful if you have smart people, but we have people that are stupid. We have people that aren't smart."
Be it Iowa, New Hampshire, Alabama or Pennsylvania, Trump has blasted the benefits of globalization. He claims deals with China, Mexico, Japan and other countries have siphoned away U.S. manufacturing jobs with nothing to show for it, and points to his own business history of outsourcing the production of his own clothing line to demonstrate that companies have financial incentives to make products overseas.
"Our politicians have aggressively pursued a policy of globalization -- moving our jobs, our wealth and our factories to Mexico and overseas," he said in a major trade speech last month in western Pennsylvania
. "Globalization has made the financial elite who donate to politicians very, very wealthy. I used to be one of them. Hate to say it, but I used to be one of them."
The issue is an integral part of Trump's populist appeal. He hopes to offset potential losses in Latino-heavy swing states like Florida, Nevada and Colorado with wins in the Rust Belt by capturing white, blue-collar workers in states such as Pennsylvania, Ohio and Michigan.
The presumptive Republican presidential nominee's top targets on the campaign trail have been the North American Free Trade Agreement, signed by President Bill Clinton, as well as trade ties with China and the 12-nation Trans-Pacific Partnership, negotiated by the Obama administration but not yet implemented.
The policy position has been a liability for his presumptive Democratic foe, Hillary Clinton -- who championed the same Pacific Rim trade deal during her tenure in President Barack Obama's administration that she now opposes on the campaign trail.
Pence, meanwhile, has a long history of voting for free trade.
Sensing an opportunity to muddy the waters on a problematic issue and blunt Trump's attacks, Democrats are set to attack Trump and Pence over their differences on trade.
"Despite their rhetorical difference on trade, Donald Trump and Mike Pence's policies are both staunchly behind helping Trump's bottom line," said Ben Ray, the communications director for the pro-Clinton Democratic opposition research shop American Bridge.
The potential problem for Trump -- who so far has escaped any punitive damage from voters for flipping his positions -- is that Pence isn't just a little squishy on trade, he's been all-in for the benefits of globalization.
In fact, he backed every free trade deal up for a vote in his 12 years in Congress. Pence voted for the Central American Free Trade Agreement, as well as trade pacts with South Korea, Colombia, Panama, Peru, Singapore and more.
He supported "fast-track" authority to allow presidents to negotiate trade deals and submit them to Congress for up-or-down votes with no amendments and under a time limit.
And -- in potentially the most problematic Pence remark on trade -- he tweeted in 2014 of his support for the Trans-Pacific Partnership.
"Trade means jobs," Pence tweeted on September 8, 2014, "but trade also means security. The time has come for all of us to urge the swift adoption of the Trans Pacific Partnership."
He also backed the deal in a letter to Indiana's congressional delegation last year -- lumping the Pacific Rim deal in with a renewal of the trade negotiating authority for Obama and a U.S.-European Union deal still under negotiation.
"I encourage your support for Trade Promotion Authority, the Trans-Pacific Partnership, the Trans-Atlantic Trade and Investment Partnership and any other trade-related measures when they are brought before the Congress for consideration," Pence wrote.
And it wasn't just in on Capitol Hill.
As governor, Pence led also led trade missions to China and Japan, touting Indiana's economic ties to the two Asian nations that Trump frequently accuses of manipulating their currencies in order to give their exports price advantages.
Pence hasn't addressed his conflicts with Trump on policy -- which also include criticism of his proposal to ban Muslims from entering the United States -- directly.
Neither the Trump campaign nor representatives for Pence immediately responded to requests for comment.
However, the Indiana governor downplayed those differences while speaking to reporters Monday in Indianapolis.
"Look, I served in Congress for 12 years. I've been a governor for three and a half years. I haven't agreed with every one of my Republican colleagues or Democrat colleagues on every issue," Pence said.
"But I'm supporting Donald Trump because we need change in this country," he said, "and I believe he represents the kind of strong leadership at home and abroad that will, to borrow a phrase, make America great again."
One of Trump's often-used campaign talking points -- the decision of Indianapolis air conditioning manufacturer Carrier to shift 2,100 jobs to Mexico -- has been a months-long headache for Pence.
USW Local 1999 President Chuck Jones told local reporters that Pence never reached out to meet with Carrier's workers -- saying Pence, who often claims credit for Indiana's job growth, should also own the failure to keep Carrier from relocating.
"If you want to take credit for all those jobs coming to Indiana, and we're losing jobs due to corporate greed -- I've got issues with that," Jones told RTV6 in Indianapolis this month
House Speaker Paul Ryan, another staunch free trade supporter, sought to bridge the gap between Trump's populist protectionism and conservatives like Pence who back trade pacts in an interview with NPR.
He pointed to Trump's comments that he doesn't oppose all trade deals
-- just poorly negotiated ones -- and said he sees that as a reason for optimism.
"The fact that he says he wants trade agreements, just good ones, I think tells me that he's not against getting trade agreements, it's just the quality of the trade agreements he wants to get. And that's fantastic," Ryan said. "I want to go get trade agreements because if America walls itself up, if we address sort of an economic fortress America, we will lose."