Jon Huntsman, the former Utah governor who recently staked his entire campaign on a strong performance in New Hampshire, was the first to issue the threat, calling it "an effort to preserve New Hampshire's historic first-in-the-nation primary status."
Former House Speaker Newt Gingrich joined Huntsman's call this afternoon.
"I will not compete in a state which holds its contest inside of one week of New Hampshire," he said in a statement.
A reporter for Manchester-based WMUR-TV said that Rick Santorum's and Michele Bachmann's campaigns were considering doing the same; their campaigns did not immediately respond to requests for confirmation.
The call is a reaction to a memo issued by New Hampshire Secretary of State Bill Gardner on Wednesday saying that he was prepared to call the election as early as Dec. 6 if Nevada insisted on holding its caucuses as planned.
"We cannot allow the political process to squeeze us into a date that wedges us by just a few days between two major caucus states," Gardner wrote, noting that state law requires seven days between New Hampshire and any "similar election" that would follow. "Our primary will have little meaning if states crowd into holding their events just hours after our polls have closed."
A similar tactic was used in 1996 when Delaware attempted to hold its primary just after New Hampshire. No candidate filed to be on the primary ballot, including then-President Bill Clinton.
Huntsman and Gingrich called on other candidates, including Mitt Romney and Rick Perry, to join their boycott. It's highly unlikely either would do so.
For Romney, Nevada is a key part of his strategy for winning the nomination -- one that also includes a victory in New Hampshire.
One of Perry's leading endorsements thus far is from Nevada's first-year governor, Brian Sandoval.
The Silver State has rejected calls to change its date, arguing that New Hampshire could avoid moving to December while still complying with state law.
"A caucus is not the same as a primary election," Sandoval told the Las Vegas Sun's Jon Ralston. "New Hampshire could easily choose Jan. 10 for its primary and still preserve the intent of its seven-day rule as it applies to primary elections."
The next candidate debate is scheduled for Tuesday in Las Vegas.