* Team appointed by Snyder slated to meet on Monday
* Michigan governor glad for more time to work out deal
* Detroit mayor undergoes surgery (Recasts with background)
By Ben Klayman
DETROIT, March 24 (Reuters) - Michigan's Court of Appeals has cleared the way for a team appointed by the governor to come up with a consent deal to keep afloat Detroit, America's historic "Motor City," which could run out of money in months.
The pressure on Detroit is intense. Monday is the deadline for Governor Rick Snyder's team to recommend what to do to fix the dire financial situation for Michigan's largest city, long synonymous with the U.S.-based auto industry.
Detroit and the state of Michigan have been negotiating to try to stave off the appointment of an emergency manager for the nearly bankrupt city.
Those talks, which continued on Saturday, were given a boost when t he court late on Friday reversed an order from earlier in the week that questioned whether the team could meet in private and barred it from issuing a recommendation until a hearing set for Thursday.
Also on Saturday, Detroit Mayor Dave Bing had successful surgery to repair a perforation of his intestines and designated his chief of staff as acting mayor while he recovers.
A spokesman for the city said Bing, 68, was resting comfortably and was still involved in talks to reach the consent agreement.
Detroit's finances have been crumbling due to a steep population drop, sinking revenue and a huge debt load.
The city has faced hard times for decades. Detroit was home to nearly 1.9 million people in the 1950s, but now has a population of about 714,000, shrinking its revenue base. With the U.S. auto industry's contraction, the city lost 25 percent of its population between 2000 and 2010.
Once the recommendations are issued, Snyder has 10 days to act. The 10-member team, which includes state Treasurer Andy Dillon, is slated to meet on Monday afternoon.
If a consent agreement is not reached, the state could cut off revenue-sharing funds or appoint an outside emergency manager to run Detroit.
A spokeswoman for Snyder said the administration was "thankful" the appeals court had allowed the review team to work toward a resolution of the financial crisis.
"Resolving this crisis in a timely matter is crucial for the residents of Detroit," Geralyn Lasher, Snyder's spokeswoman, said in a statement.
Snyder has said repeatedly he does not favor the option of appointing an emergency manager for Detroit.
Bing, who is expected to remain in the hospital for five to seven days, can resume limited administrative duties as early as Sunday, a city spokesman said.
Opponents of any kind of state takeover of the city were disappointed.
"We obviously are still very, very concerned about state occupation of Detroit," Rainbow Push Detroit President Reverend D. Alexander Bullock said. "I'm worried that now there will be a top-down, paternalistic approach to public policy that will displace the democratic process."
Andrew Paterson, an attorney for Robert Davis, a local school board member and union activist who challenged the financial review team in court, said, "We will review this hastily issued order and will be considering our legal strategy."
Detroit's long-term liabilities are estimated to top $12 billion, while the city's annual budget is put at about $3.1 billion.
Both Fitch Ratings and Moody's Investor's Service slashed the city's ratings and said more cuts were possible as the city and the state of Michigan struggle to agree on a plan to keep the city from running out of cash.
On Friday, roughly half of Detroit's unionized public employees accepted pay cuts and other concessions to save $68 million a year, actions a spokesman for Snyder said did not go far enough to address the city's long- and short-term troubles.
The agreements announced on Friday did not include Detroit's police and fire unions, which also had tentative deals.
Reporting By Ben Klayman, Tiziana Barghini and David Bailey; Editing by Peter Cooney