Former South Carolina governor Mark Sanford also joined the GOP presidential primary race over the weekend, bringing to three - along with Walsh and former MA governor Bill Weld - the number of notional 2020 rivals to Trump.
A SC state party official said there would be savings to taxpayers, and listed years when either Democrats or Republicans in the state didn't hold primaries when their party held the presidency.
An optimistic Weld told Fox News that "we already have our first televised debate signed up for and that's going to add a new dimension to the race and I think it's going to be harder and harder for the Trump forces to ignore the fact that 2020 is an election year".
Sanford, 59, is the third Republican to announce his intention to run against Trump - joining former MA governor Bill Weld and former IL congressman Joe Walsh.
In addition to the constraints imposed by limited financial support, there's no indication that a majority of Republicans have much interest in changing direction on policy.
Sanford, who announced his candidacy on Sunday, said he did not believe Trump's popularity would last.
President Trump is betting that his political brand will help Republicans keep hold of a North Carolina U.S. House seat in a special election Tuesday.
However, although Sanford has been a frequent critic of Trump, he has said he would back the President instead of a Democrat.
William (Bill) Weld is an American attorney, businessman, and Republican politician who served as the 68th Governor of MA from 1991 to 1997. "The country is sick of this guy's tantrum - he's a child", responded Walsh to Stephanopoulos when he pointed out the massive uphill climb Walsh has in front of Trump in the 2020 primary.
President Trump mocked his Republican challengers on Monday, calling them "The Three Stooges".
The Republican National Committee does not require candidates to appear on primary ballots in all 50 states. Michael Blitzer, a political science professor at Catawba College in North Carolina asked ABC News. "I think it's getting less close", Trump said.
Should Sanford decide to run, the South Carolina GOP's decision to drop its 2020 primary would certainly hurt his chances in the state where he is best known.
Tuesday, actress and activist Mia Farrow of Rosemary's Baby fame tweeted a New York Times opinion piece penned by Republican strategist Liz Mair, in which Mair lays out why she thinks the former S.C. governor warrants the greatest threat to Trump's re-election bid.
"Is the presidential rhetoric of the past month, going to do damage to the Republican candidate that has basically embraced the president?" Canceling nominating contests is not unusual for the party that controls the White House when an incumbent president is seeking a second term.
Former Illinois Rep. Joe Walsh said it was "undemocratic".
In a tweet after making his announcement on Sunday, Sanford said he respects the views of his Republican friends who have suggested that he should not run, but that "competition makes us stronger".
President Trump went down to Dixie again in hopes of salvaging a North Carolina Congressional seat where a GOP candidate is locked in a tight special election battle.
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