It turns out that registering is as easy as asking for a ballot on Ohio's primary day. So, he told them, just show up on March 15, and request a Republican ballot. So they did.
In Mahoning County, home to Youngstown, one of the great steel cities of the early 20th century, 6,171 Democrats did this. Fewer than 200 Republicans wanted to become Democrats.
"I looked at Republican turnout on election night and I saw 34,000 Republicans had voted," Monroe said. "I nearly fell off my chair because there were only 14- or 15,000 Republicans in Mahoning County."
Most shocking of all, is that 18 Democratic precinct captains -- local party officials in the county -- were among the switchers. Dave Betras, the county Democratic chair, summarily fired them.
"I just simply with the stroke of a pen removed them and filled their positions with other loyal Democrats," he said.
If Donald Trump can win Ohio in November, it'll be because of places like Mahoning County. He badly lost the Ohio primary to Gov. John Kasich, but he won in Mahoning County.
It should also be noted, however, that Hillary Clinton won big here, too. She got 21,000 primary votes, nearly 60% of county's Democratic primary votes. Trump got 17,139 primary votes, 50% in the Republican primary.
Democrats of Mahoning County, until this year at least, have been loyal. President Obama beat Mitt Romney here by 28 percentage points four years ago. He topped Arizona Sen. John McCain by 26 percentage points in 2008. The county hasn't voted for a Republican in a general election since Richard Nixon in 1972. Even then, the area's heyday had long since passed.
A Depression-era magazine advertisement billed Youngstown as the "city of homes." As the steel mills cranked out necessities for both life and war, Mahoning County prospered, as did its ballooning middle class.
But that all changed on Black Monday, September 19, 1977, a date forever etched in the minds of Youngstonians. That was the day the first mill, Campbell Works Mill, closed its doors. Soon others followed.
"Over that period of time unemployment continued to rise to the point in late 1982 there were something like 25 percent unemployment in this metropolitan area," said John Russo, a local historian and professor at Youngstown State University. "The unemployment rate dropped very quickly, but it was because people were leaving. They were no longer counted."
Today, Youngstown's population stands at 67,000. Less than a third of what it once was. Unemployment is marginally higher than the national average, but that could simply reflect a workforce that has given up.
"Mahoning County is a shell of its former self," said Debbie Taylor, 62, who was born in Youngstown.
Taylor ran for county commissioner in 2000 as a Democrat. Four election cycles later, she's one of the switchers: No longer a Democrat, she's voting for Donald Trump.
"I was one of the people that never, never thought he would have the temperament or the ability," Taylor said. "The more he talked and the more everybody said, 'He's not a Republican, he's not a Republican,' it started to hit me. He's an American ... and when I believed that he had the ability to pull it off, I was 100 percent behind him because I believe in his message and I believe in what he stands for."
It's a common refrain heard from Trump loyalists across the county -- we need to bring back trade skills. But few places would such a policy have such a profound impact as the rust belt and counties like Mahoning.
Denise Cooper and Denny Zimmit both had family members lose their jobs at the steel mills. Zimmit remembers when his grandfather's employer walked away from his pension.
"I can't say it actually killed him but when you just lose everything you have, and you're 70-some years old, what are you going to do?" he says. "When you're 70, after working in the mills all those years, you're pretty beat up."
"Donald Trump said he wants to bring things back. He's going to bring things back and I believe that we all have to take a little bit of concessions somewhere along the line to bring back our steel, to bring back our trades."
Some 6,000 party switchers may qualify as a phenomenon, but Chad Jones, who is retired from the Air Force and now a door-to-door vacuum cleaner salesman, was surprised for another reason.
"It's only 6,000? Wait until the general election. You just wait," he said. "When they go to general, there'll be probably double, maybe triple that amount are going to switch."
Monroe, the Republican chairman, is optimistic.
"I think it's possible that Donald Trump can actually carry Mahoning County," he said. "If [he's] able to carry Mahoning County, I think he wins the White House."
That's a pipe dream, says Betras, the local Democratic chairman.
"The people here are just not going to buy [Trump's] bullsh--t," he said. "They're more sophisticated than that."
"I know these people will come back."