And now, some in New Hampshire have tried to defend their state from the rumors.
"It is un-presidential. It's inappropriate," Todd Selig, town manager of Durham, New Hampshire, told CNN on Monday. "If he has proof, bring forward his proof. If not, then please stop saying it, because it's just wrong."
Unfounded voter fraud claims have swirled for years in New Hampshire, with people warning about illegal, out-of-state voters.
They date back to the 1990's, when then-Gov. Steve Merrill, a Republican, instituted same-day voter registration, and they continued through the 2016 election. Just days before the most recent election, Chris Sununu, who was then a candidate and now the sitting governor, said Democrats
were busing in voters to win the election.
Although there have been prosecuted cases of voter fraud in the past, there has been no evidence of mass voter fraud that could come close to swinging election. Sununu has since walked away from that claim, and on Monday his office issued a statement
to local broadcaster WMUR saying he was "not aware" of any widespread fraud.
Now with Trump, those unfounded rumors have been elevated to the presidential level.
Criticisms pile on after claims made
In a private meeting with senators last week, Trump was said
to have claimed buses of people from Massachusetts were able to vote in New Hampshire and swing the state for the Democrats, causing his and former Sen. Kelly Ayotte's losses there. An FEC commissioner responded after reports of the meeting emerged, calling on him
to provide evidence for the "extraordinarily serious and specific charge."
White House policy director Stephen Miller reiterated
those claims Sunday, saying: "Go to New Hampshire. Talk to anybody who's worked in politics there for a long time. Everybody's aware of the problem in New Hampshire."
But many people in New Hampshire responded, voicing confusion and anger.
Former New Hampshire GOP chairman Fergus Cullen took to Twitter to offer a $1,000 reward for evidence of a single illegal vote from Massachusetts. He said no one had offered evidence, and in an interview on Monday with CNN's Brooke Baldwin, he blasted the White House's claim.
"The idea that people are coming to New Hampshire to commit fraud on a massive scale like this is just preposterous and it needs to be called out as untrue," Cullen said.
The New Hampshire secretary of state's office said it had not received any complaints of voter fraud.
And a few voters in the snow-covered state also had icy responses to the White House's claims.
Al Hotaling, a registered independent who said he wrote in former Vice President Joe Biden in the 2016 election, called the busing claim "balderdash."
While Trump and the White House's claims about mass voter fraud have been loud, they have yet to back them up with evidence or announce actions taken on their behalf.
The White House did not immediately respond to a CNN request for comment.
As of Monday, Trump had yet to sign an executive order examining the vote. Despite claiming he would have Vice President Mike Pence lead a commission to investigate it, the White House had yet to announce the actual formation of such a commission. And his campaign never called for a recount of the vote -- instead, fighting the recount campaigns in several states.
White House press secretary Sean Spicer on Monday said the lack of action so far was because the White House needed to confer with Attorney General Jeff Sessions, who was just confirmed last week.
"Sessions just got sworn in. The vice president's probably going to be talking to him, and while I don't have anything now, I know that should be something we have more on in a little while," Spicer said.