HOUSTON (Reuters) - Hess Corp ( HES ) CEO John Hess has until Tuesday to quell a rebellion by shareholders over his handling of what could turn out to be one of the largest mergers in oil industry history: a proposed $53 billion sale of the oil producer to Chevron Corp. ( CVX )

Hess, 70, has spent the past month visiting or calling dozens of investors to gather support. The sale seemed all but certain last fall and Hess still appears poised to win, based on Reuters' interviews with large investors. But support has slipped in recent weeks with more investment funds voicing concerns about the deal.

A lengthy U.S. federal regulatory review and a surprise arbitration challenge from Exxon Mobil ( XOM ) have put about 40% of shares outstanding on the fence, interviews show.

That could make it harder for Hess to get more than 50% of the 308 million shares outstanding to win approval, even though he can count on his family shares along with other directors and management, for about 10%.

Hess has lost about $5 billion in market value since the deal was announced. Every quarter the merger is delayed, its shareholders lose the chance for a dividend payment from Chevron ( CVX ) -- a major incentive since Chevron's ( CVX ) dividend is four times bigger than the Hess payout.

"This is the mother of all embarrassments," said a London-based investor who declined to be named, adding that if Hess shareholders approve this deal, chances will fade for a higher bid.

TIGHT SCOREBOARD

Three firms - HBK Capital Management, D.E. Shaw & Co, and Pentwater Capital Management - have stated they are not ready to give their go ahead. Together they hold almost 6% of Hess.

Another three investors filed lawsuits to delay or block the vote, backed by a flood of letters to Hess management complaining it failed to disclose legal and regulatory issues that could delay the transaction by up to one year.

Six large investors who spoke with Reuters under condition of anonymity estimated firms holding about 40% of the company's stock have decided or are strongly considering abstaining, essentially a no vote.

"The longer this takes, the more I would begin to question the value proposition of this merger," said Roy Behren, co-president of Westchester Capital Management, which holds $317 million in Hess shares and is considering an abstention.

The delays have shrunk expected profits for arbitrage funds that pounced on Hess shares after the deal was announced betting it would close in the first quarter.

Fayez Sarofim & Co, Invesco ( IVZ ) and Barrow Hanley which hold some 3% of outstanding shares worth about $1.5 billion, are expected to vote yes, according to people familiar with the matter. The three firms declined requests for comment.

Influential proxy advisor Institutional Shareholder Services (ISS) has recommended abstention to give more time for details of the arbitration case to emerge. Rival Glass Lewis, recommended a vote in favor, saying the Chevron ( CVX ) deal merits are sound and offer Hess shareholders a premium.

Top investment firm Vanguard Group, with 10% of Hess shares, holds the largest individual stake. Votes of its portfolio managers could swing the outcome. Vanguard declined to disclose its vote.

EXXON AS POSSIBLE SPOILER

This year, Exxon and partner CNOOC Ltd filed an arbitration case claiming they have a first right of refusal to buy Hess' Guyana assets. Chevron ( CVX ) and Hess say a right of refusal does not apply to sale of the entire company. If Exxon's arbitration succeeds, Chevron ( CVX ) could walk away from the deal without paying a break up fee.

In recent private meetings, John Hess told investors he did not know Exxon's end game with the arbitration. If Exxon succeeds, Hess and Chevron ( CVX ) say they would call off the deal, and Hess said this would mean Exxon could not exercise its right of first refusal on the Guyana assets.

If the arbitration succeeds and Chevron ( CVX ) walks away, Hess would have few alternate buyers given the pre-emption right to any future deal, said Biraj Borkhataria, an energy analyst with researcher RBC Capital Markets.

Chevron ( CVX ) sorely needs the deal to keep up with rival Exxon, which this month closed its $60 billion acquisition of shale producer Pioneer Natural Resources.

The lucrative Guyana oilfields from Hess would help Chevron ( CVX ) hedge geopolitical risks associated with TengizChevroil project in Kazakhstan, which moves most of its oil across Russia to a Black Sea port. It would also help balance overruns at Chevron's ( CVX ) Australian liquefied natural gas (LNG) projects, hit by labor and operating troubles.

A spokesperson said Chevron ( CVX ) "looks forward to Hess obtaining a successful shareholder vote and completing the transaction on the terms of our merger agreement." Last month, CEO Michael Wirth said Chevron ( CVX ) would be in good shape regardless of the acquisition.

Some Hess shareholders wonder if Exxon would make a higher offer for the Guyana assets than what they would get from Chevron's ( CVX ) bid for the company. There are no legal impediments to an Exxon offer before Tuesday, but Exxon has said it wanted to have its rights over the Guyana asset affirmed before making any decision on a bid.

Exxon has also said it would not seek to acquire Hess as a whole.

"I don't see how Exxon can bid (for Hess) when they have said they would not," said oil analyst Paul Sankey, from Sankey Research firm. "Unless they wait a while, and things change a lot. I mean years."