By Jason McLure

LITTLETON, New Hampshire (Reuters) - Pressure is mounting on Nevada's Republican Party to push back its presidential caucus as four candidates announced they could boycott the contest, standing in solidarity with New Hampshire.

Minnesota Representative Michele Bachmann, former Utah Governor Jon Huntsman, former House Speaker Newt Gingrich and former Pennsylvania Senator Rick Santorum have all said they may skip the caucus to support New Hampshire's traditional status as an early primary state.

Huntsman also said he would boycott Tuesday's Republican debate in Las Vegas and instead hold a town hall meeting in New Hampshire, where he has been campaigning heavily.

Nevada and New Hampshire are among four states authorized by the Republican National Committee to hold the first contests on the road to choosing a nominee to face Democratic President Barack Obama in the November 2012 election.

Aiming to protect the state's status as one of the earliest contests in the race, Nevada Republicans pushed up their caucus by more than a month to January 14 after Florida bumped its primary in a move that left the nominating process in turmoil.

But Nevada's move irked New Hampshire, which traditionally holds its primary ahead of Nevada's caucus. Under current plans, Iowa is tentatively scheduled to hold its first in the nation caucus on January 3, with the Nevada caucus penciled in for 11 days later.

Not wanting to be boxed in, New Hampshire's Secretary of State has threatened to hold the state's primary as early as December 6 unless Nevada pushes its caucus back.

New Hampshire traditionally holds its primary on a Tuesday, and state law requires it to hold its contest seven days before any "similar" contest.

A move by Nevada to push its caucus back by three days to January 17 could allow New Hampshire to hold a primary on January 10 and still have a one-week space before Nevada's contest.

HUNTSMAN CRITICIZES ROMNEY

If Nevada sticks with its January 14 caucus, the latest New Hampshire could hold its primary would be January 7, a Saturday, and just four days after Iowa -- something state officials have said would diminish the Granite State's status.

Huntsman kept up his criticism of Republican front-runner Mitt Romney, who he accuses of encouraging Nevada to have an early caucus in order to consolidate his lead in the polls.

"While Mitt Romney's campaign has tried to game the system by encouraging Nevada to move to an earlier date, Governor Huntsman is sticking up for the Granite State," a statement from the Huntsman campaign said.

A spokesman for the Nevada Republican Party did not respond to messages about the state's plans.

Romney and Representative Ron Paul have said they will compete in Nevada, as has Texas Governor Rick Perry who has the backing of Nevada Governor Brian Sandoval, giving him a boost in a state that backed Obama in 2008.

A spokesman for former businessman Herman Cain, who has surged close to or even ahead of Romney in some national polls, did not respond to messages.

This year's Republican selection calendar was compressed when Florida announced in September that it would hold its primary January 31. South Carolina then jumped its "first southern state" primary to January 24.

Gingrich issued a statement late on Thursday saying he would likely skip Nevada, but a spokesman for his campaign on Friday hoped for a compromise.

"We want to campaign in Nevada and there are five Tuesdays in January," said Joe DeSantis, Gingrich's communications director. "There ought to be a way to work this out."

(Reporting by Jason McLure, editing by Ros Krasny and Cynthia Johnston)