WASHINGTON (Reuters) - As Republican leaders desperately seek ways to derail the presidential campaign of billionaire Donald Trump, many of the party’s 31 state governors are staying out of the fray.  New Mexico Governor Susana Martinez endorsed Marco Rubio on Friday, making her only the 10th governor to back one of the four Republican presidential rivals left in the race. Much more typical is Governor Rick Scott of Florida, who said on Thursday he would not endorse a candidate before his state’s hotly contested March 15 primary. Such reluctance to commit contrasts sharply with previous elections, when governors lined up solidly behind eventual nominees, helping to winnow the field of candidates early on. The 2016 election differs because a chaotic race has divided Republicans, convincing many to keep a low profile in hopes of avoiding a possible backlash from voters who are increasingly contemptuous of party leaders, Republican officials say. “It’s a lose-lose political situation,” said Fergus Cullen, a former New Hampshire Republican Party chairman. New Jersey Governor Chris Christie last week took a risk, after dropping out of the presidential contest himself, and endorsed Trump, the billionaire businessman. That decision has done little for either of them, according to a new poll. Almost two-thirds of 1,372 adults polled, both Republicans and Democrats, said Christie’s endorsement made no difference in their feelings toward Trump, the Republican front-runner. The nationwide Reuters/Ipsos poll was conducted Feb 29-March 4. Christie has faced relentless criticism since he announced his support for Trump last week. Six newspapers in his home state have called on him to resign. In past elections, a governor’s endorsement could produce a burst of positive news coverage and the support of well-connected local leaders for a presidential contender. That would encourage other elected officials to endorse the candidate as well, creating an impression that the candidate was a favorite of those who knew best and encouraging others to drop out of the race, said David Karol, a University of Maryland political science professor who has found that endorsements were a strong predictor of electoral success between 1980 and 2004. “The absence of most of the governors this late in the process really indicates the paralysis and division in Republican elite circles,” Karol said. Ahead of Election Day on Nov. 8, many governors did not want to talk about Trump, who has unnerved his party’s establishment with his abrasive tone and policy positions, including plans to build a wall on the U.S.-Mexican border, deport 11 million illegal immigrants and temporarily bar Muslims from entering the country. Eighteen undecided Republican governors, contacted by Reuters, declined to be interviewed on their views of the race.  National Republican leaders are struggling for a strategy to stop Trump from becoming the nominee, as Democrats revel in the chaos they hope will boost their chances of keeping the White House. George W. Bush, elected president in 2000, had the support of 26 of the party’s 30 Republican governors before primary voting even started, according to figures compiled by James Madison University political science professor Martin Cohen, who with Karol is a co-author of “The Party Decides: Presidential Nominations Before and After Reform.”  In 2012, 10 of 29 Republican governors had endorsed Mitt Romney by the time he clinched the presidential nomination. This year, governors are not sending a clear signal to voters. Five have endorsed Rubio, a senator from Florida who has won one nominating contest so far. Two have endorsed John Kasich of Ohio, the only governor left in the race, who has won no contests. Two have Trump. One has backed Senator Ted Cruz of Texas. Three others endorsed candidates who have since dropped out of the race. The governors who have made endorsements so far have had little impact. Rubio lost in Tennessee, South Carolina and Arkansas, despite the backing of governors in those states. Kasich got only 4 percent of the vote in Alabama on Tuesday after that state’s Governor Robert Bentley endorsed him.  Iowa Governor Terry Branstad called on voters in his state to reject Cruz before the state’s February caucuses. Cruz won. So far, only Texas Governor Greg Abbott has picked a winner. He endorsed Cruz, who won Texas on Tuesday. Trump has put many governors in a difficult position. The real estate developer is expected to easily win Mississippi’s Republican primary next Tuesday, for example, but his support for Planned Parenthood and government-backed health insurance, among other policies, put him at odds with the conservative positions backed by Governor Phil Bryant. Bryant will support Trump should he end up being the party’s nominee, but he has not decided whether to endorse a candidate before the primary, an aide told Reuters.  In theory, governors should be in a position to shape the outcome of this year’s nominating contests. Republicans at the state level have delivered tax cuts, abortion restrictions and other conservative victories from Maine to Arizona, while their counterparts in charge of Congress have been locked in a stalemate with Democratic President Barack Obama. But the plethora of establishment-minded candidates this year has made it more difficult for governors and other senior officials to decide who to back, let alone try to shape the outcome with an endorsement.  Republican governors in Maryland, Florida, Wyoming, Indiana, Wisconsin, North Dakota, South Dakota, Arizona, Nebraska and Michigan declined to say whether they would back Trump if he were the party’s nominee.  Governors in Utah, Oklahoma, North Carolina and Georgia have yet to endorse a candidate but would back Trump if he won the nomination, aides said.     Massachusetts Governor Charlie Baker told reporters this week he would not vote for Trump in November.  (Additional reporting by Nick Carey, Sharon Bernstein, Ian Simpson, Alex Dobuzinskis and Scott Malone; Editing by Kevin Drawbaugh, Howard Goller and Alistair Bell) This article was funded in part by SAP. It was independently created by the Reuters editorial staff. SAP had no editorial involvement in its creation or production.