Washington – A long-awaited $50.5 billion Hurricane Sandy-relief bill is heading to President Obama for his signature — and with that comes the start of competition for the money among the governors of Connecticut, New York and New Jersey, as well as governors of other states.

“The real fight is just beginning, and we must make sure Connecticut gets its fair share,” said Sen. Richard Blumenthal, D-Conn.

The Sandy relief bill was approved by the Senate 62-36 Monday after senators rebuffed an attempt to require its $50.5 billion cost to be offset by cuts to federal programs.

Blumenthal said Connecticut’s request to the White House — $3.2 billion — is “relatively small” and likely to be approved by federal agencies that will now distribute billions of dollars to Sandy-hit states.

But how much money will go to Connecticut is still unknown and may be less than Connecticut Gov. Dannel P. Malloy wants.

Most of Malloy’s request, $2.5 billion, is to bury power lines and for other power transmission upgrades.

Dan DeSimone, head of Connecticut’s Washington office, said the state hopes to bury the electric lines in “selective, high-density areas” mainly, but not exclusively on the coast.

But the Sandy-relief bill does not include a specific provision for that money.

No matter, DeSimone said, some of $16 billion in Department of Housing and Urban Development Community Disaster Block Grant money could be used to bury power lines.

“CDBG funds are flexible and could be used for energy infrastructure projects,” DeSimone said.

HUD spokesman Brian Sullivan said the burial of power lines would qualify for CDBG funds, which are meant to be used for housing and infrastructure.

“If you asked a public utility to do so, that could lead to controversial rate hikes,” Sullivan said.

Yet odds are against Connecticut’s receiving all of the money it has asked for. Malloy’s $3.2 billion request is for mitigation efforts, not reconstruction. Besides burying power lines, Malloy wants to build new seawalls and relocate sewage treatment plants.

But those projects may carry less weight than requests from other Sandy-hit governors, who asked for a total of about $70 billion to make their states whole.

Blumenthal, who toured storm-hit areas in Bridgeport Monday, said a good case could be made that storm walls, dikes, pumping stations and other mitigation efforts would save the federal government money in the long run because they would prevent massive flooding.

“That’s the kind of protection that could help Bridgeport and other areas,” he said.

Although coastal areas in Connecticut were devastated by Sandy, New York and New Jersey suffered far more extensive damage to more highly populated areas.

That may also hurt Connecticut’s chances. HUD has been mandated to distribute grant money to the “most impacted and distressed areas.”

The Sandy bill has also made cities and states that suffered disasters in 2011, 2012 and even this year eligible for the $16 billion pot of money, making competition for the funds even tougher.

Stephen Ellis, vice president of Taxpayers for Common Sense, a budget watchdog group, said that makes nearly every state eligible for the money. Only South Carolina, Arizona and Michigan don’t qualify, he said.

Nevertheless, DeSimone said he’s confident Malloy will receive what he has sought from HUD and other agencies.

The disaster relief bill also provides billions of dollars for transportation and Army Corps projects. But once again, federal agencies will distribute the funds according to need and formulas that consider whether a project would save more money than it costs.

The House approved the disaster relief bill earlier this month. Both chambers also approved $9.8 billion to replenish the national flood insurance program — which was also hard hit by Sandy — earlier this month.

The Sandy bill contains $18 million to repair the Coast Guard Academy in New London.

But, saying nobody visits the refuge, Rep. John Fleming, R-La., succeeded in stripping from the bill $9.8 million the Malloy administration had asked for to repair damage to the Stewart McKinney Wildlife Refuge in Stratford.

No money earmarked for any other state was stripped out of the bill, prompting Connecticut lawmakers to complain that their state has Cinderella status when it comes to Sandy funds.

“I voted for the bill and am pleased it will provide much-needed relief for Connecticut, but this was a vindictive amendment that needlessly slashes disaster relief for one particular state,” said Rep. Rosa DeLauro, D-3rd District.

Malloy, Cuomo and Christie joined forces in pressuring Congress to approve the Sandy bill.

“By helping each other, we help the whole,” Cuomo said.

Now the governors will have to lobby federal agencies for reconstruction money on their own.