* Eighty Republicans back shutdown strategy on Obamacare
* Republicans consider using debt limit to delay law
* Boehner to hold conference call with Republican lawmakers
By Caren Bohan and Rachelle Younglai
WASHINGTON, Aug 22 (Reuters) - Republican leaders of the U.S. House of Representatives are working to prevent their ranks from fracturing over the strategy of threatening a government shutdown to gut President Barack Obama's signature healthcare law.
About a third of the Republican caucus sent a letter to House Speaker John Boehner and Majority Leader Eric Cantor on Thursday, urging them to oppose any annual spending bills that include funding for the health law known as "Obamacare."
"We look forward to collaborating to defund one of the largest grievances in our time and to restore patient-centered healthcare in America," said Representative Mark Meadows of North Carolina, who rallied support for the letter signed by 80 House Republicans.
The strategy could lead to a government shutdown on Oct. 1, which is the deadline Congress faces to pass a broad spending measure to keep the government funded.
Obama would need to sign any spending bill that Congress puts forth, and even many Republicans doubt he would ever sign a measure that removed funding for Obamacare.
Many Republicans fear they would be blamed if the government were to shut down, leading to a backlash in the 2014 congressional elections. Republican leaders, including Boehner and Cantor, are wary of the strategy of threatening a government shutdown over Obamacare even though they share with Meadows a distaste for the health law.
But Meadows and his allies see the funding bill as one of the last chances to stop Obamacare before major provisions of it are rolled out this fall and at the start of next year.
Prominent Republican senators such as Ted Cruz of Texas and Marco Rubio of Florida also favor denying any funds for the law.
With the party divided, Republican leaders have been working to find alternative ways to try to weaken the health law.
One idea under consideration is tying approval of an increase in the country's borrowing limit to agreement by the Obama administration to delay implementation of the law.
Boehner was due to hold a conference call with Republican lawmakers later on Thursday in which Obamacare is expected to be raised. The debt limit idea could come up though it may be weeks before House leaders finalize their strategies on both the health law and the fall fiscal battles.
The government is on track to reach its statutory borrowing limit around November, according to the latest analyst forecasts. If the debt limit is not raised by then, the country could face a catastrophic default on its credit obligations.
Obamacare is riling up crowds in lawmakers' home districts as they meet with constituents during a five-week summer break.
In an effort to get House Republicans to deliver the same message, leaders sent members talking points that included the chamber's long list of efforts to kill Obamacare.
"It is also important to remind your constituents that cracks in Obamacare are growing and getting deeper," said the memo sent by House Majority Whip Kevin McCarthy and House Republican Conference Chair Cathy McMorris Rodgers.
Republican aides described the memo as a refresher on what the House has already been doing to dismantle the health law.
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For months, House Republicans have tossed around ideas on how to use the debt ceiling deadline to extract budget concessions from Obama and his Democrats.
Members agree with the rule set by Boehner that any debt limit rise must be matched by budget cuts and program reforms. They have discussed tying the debt limit to everything from tax reform and revamping retirement benefits to defunding Obamacare.
The Republican caucus had yet to coalesce around a specific idea. But as momentum built around using the spending bill to stop funding the healthcare law, Republican leaders started seriously considering a strategy involving the debt limit.
An aide to Cantor, the No. 2 House Republican, told Reuters on Wednesday that the debt limit was a good "leverage point" to try to force action on Obamacare.
Republican Representative John Fleming, who signed the Meadows' letter, said he was receptive to a debt limit strategy but was adamant in wanting to fully gut Obamacare.
Ahead of Boehner's call, Fleming told Reuters that "Obamacare is despised" in his Louisiana district. The top three concerns for his constituents, he said, were "Obamacare, Obamacare and Obamacare."
White House spokesman Josh Earnest said it was "disappointing but hardly surprising" that Republicans would consider tying the debt limit to a delay in Obamacare.
But Earnest reiterated the White House position that Obama has no intention of allowing the debt limit to be used as leverage in a political fight. "The full faith and credit of the United States of America is not a bargaining chip," Earnest told reporters as he traveled with Obama to Buffalo, New York.