UPDATE (April 15, 5:10 p.m.): Former Massachusetts Gov. Bill Weld announced that he is officially running for president, which makes him the first Republican to challenge President Trump for the GOP nomination.
From ABC News:
Weld to challenge Trump for nomination
Here’s a blast from the past: Bill Weld is running for president. Speaking in New Hampshire on Friday, the former Massachusetts governor announced that he was forming an exploratory committee to seek the Republican nomination for president. Weld ran for vice president in 2016 on the Libertarian Party ticket, but he’s working within the two-party system this time. That’s smart in one sense — it’s extremely hard to win as a third-party candidate in the United States — but Weld also faces steep odds in challenging the sitting president in a GOP primary.
In all likelihood, President Trump would crush any Republican who tries to primary him. An incumbent president has not lost a bid for renomination since Chester A. Arthur at the GOP convention in 1884 — meaning that it’s never happened in the modern era of presidential primaries. And Trump enjoys a higher approval rating among members of his own party even than recent presidents who cruised to renomination, like Ronald Reagan and Barack Obama. (In a recent Fox News poll, 87 percent of Republicans approved of his job performance.) And in early, hypothetical polls of the Republican presidential primary in 2020, Trump has massive leads on even well-known opponents such as Mitt Romney, though Romney has given no indication he’s considering a run. No poll so far in our database has tested Trump against the relatively unknown Weld.
Indeed, Weld seems like one of the weakest candidates that anti-Trump Republicans could put up in a national campaign. Pretty much ever since he was elected governor of Massachusetts in 1990 and re-elected by a record margin in 1994, Weld has been the poster child for patrician, moderate, New England Republicanism. Once roasted for having ancestors who came to America on the Mayflower, Weld quipped, “Actually they weren’t on the Mayflower. They sent the servants over first to get the cottage ready.”1 Both as governor and in the two decades since he left office, Weld has supported gay rights and legal abortion alongside spending and tax cuts. According to his issue matrix at OnTheIssues, which assigns an ideological grade to politicians’ statements and votes, Weld is a progressive-leaning libertarian:

The problem for Weld is that there is no longer a demand for his type of Republican, especially at the federal level: 14 Republicans represented New England during the 104th Congress (1995-96), but only one (Sen. Susan Collins of Maine) does so today.

Even current Massachusetts Gov. Charlie Baker — a popular New England Republican and a former Weld protégé — is having trouble connecting with the national party these days: Although Baker won re-election last year by a 33-point margin, in a poll taken days after the election, Bay State Republicans sided with Trump over their governor in a theoretical 2020 primary faceoff, and Baker has grappled for control of the state party with the pro-Trump faction of the GOP. Nowadays, Baker’s base is as much Democrats and independents as it is Republicans.
As the national GOP has moved to the right in recent decades, liberal Republican voters who share Weld’s ethos have left the party behind. Many of the cities and towns where Weld performed best in his 1990s races are now solidly Democratic. Indeed, the last time Weld ran a successful election was 1994. That’s a lot of rust to shake off. And there is some evidence that candidates are less successful when they try to jump back into politics after a long hiatus. (Discounting his vice-presidential run, the last time Weld ran for office was 2006, when he ran for governor of New York but dropped out after a poor showing at the Republican convention.)
I’m skeptical that Weld will make any kind of splash in the Republican presidential primary. But if he does, it will probably be in New Hampshire. Eighty-four percent of New Hampshire residents live in the Boston media market, as Weld has for most of his life. And candidates from neighboring states tend to do well in the New Hampshire primary — just ask former winners Bernie Sanders of Vermont and Mitt Romney, John Kerry and Paul Tsongas of Massachusetts. Moderate Republicans or “mavericks” have also historically found support in New Hampshire, where independent voters (who might identify more with Weld’s party-switching) often make up more than 40 percent of the GOP primary electorate. By contrast, the GOP contests in Iowa and South Carolina are more dominated by evangelicals — definitely not Weld’s speed.
But Trump is also pretty mavericky, and his support among New Hampshire Republicans remains strong according to both polls and activists on the ground. The smart bet is still that he wins New Hampshire again.
Weld’s performance in the Granite State, however — does he win 10 percent of the vote there? 30 percent? — will provide a hint about the feelings of a group of voters that Trump will need behind him in the 2020 general election: independent voters who previously cast a ballot for him. Trump carried independent voters by 4 percentage points in 2016, helping him to eke out an Electoral College victory. If Weld finds a foothold in New Hampshire, that could suggest that Trump is struggling with those voters. That might not hand Bill Weld the GOP nomination, but it could foreshadow trouble for Trump in the general. Remember: All three incumbent presidents to face serious primary challenges during the modern primary era went on to lose in the fall.