* In call with Republicans, speaker recalls backlash from 1990s shutdown
* Republicans deeply divided on strategy to stop or weaken health law
By Caren Bohan and Rachelle Younglai
WASHINGTON, Aug 22 (Reuters) - U.S. House of Representatives Speaker John Boehner warned rank-and-file Republicans in a conference call on Thursday against using the threat of a government shutdown to stop the implementation of Obamacare, according to people on the call.
In the call, Boehner reminded Republicans of the political backlash their party suffered when the government shut down in 1995-1996, according to one person on the call.
Another participant in the call, Oklahoma Representative Tom Cole, said the speaker's main message was that he and other leaders were still committed to killing President Barack Obama's signature health care law but that they did not want a government shutdown.
Republicans agree strongly on their opposition to Obamacare, viewing the law as a burden to businesses that will cost jobs.
But the party has been roiled by heated debate over the strategy for trying to stop the law.
Hours before Boehner's conference call, about a third of the Republican caucus sent a letter to Boehner and Majority Leader Eric Cantor urging them to oppose any annual spending bills that include funding for Obamacare.
Without an agreement between Congress and Obama on fresh legislation to fund federal agencies, the government could shut down on Oct. 1. Even many Republicans believe Obama would never agree to sign a spending bill that removed funding for his signature domestic policy achievement.
Cole disagrees with the idea of using a government shutdown threat to try to take aim at Obamacare but added, "the frustration is how do you keep fighting it without taking an action that is counterproductive."
On the call, Boehner sketched out a plan in which Republicans would pass a short-term measure to fund the government until around December while insisting on keeping in place steep cuts in spending known as the "sequester."
When Congress reconvenes on Sept. 9 after its summer break, Boehner said, "Our intent is to move quickly on a short-term continuing resolution that keeps the government running and maintains current sequester spending levels."
Earlier on Thursday, about a third of the Republican caucus sent a letter to Boehner and Majority Leader Eric Cantor urging them to oppose any annual spending bills that include funding for Obamacare.
The letter was spearheaded by Representative Mark Meadows of North Carolina and got the signatures of 80 House Republicans.
During the call, one member asked Boehner, "Can you at least announce that you want to defund Obamacare?" Another asked Boehner how he would get a short-term spending measure passed, according to one person on the call.
Congressional Republicans have sought repeatedly to repeal the law.
While Republicans say the law will hurt job creation, supporters view it as a landmark initiative that will extend health insurance coverage to millions of Americans.
In addition to the House lawmakers who signed the letter to Republican leaders, there is support for denying funds to Obamacare from prominent Republican senators including Ted Cruz of Texas and Marco Rubio of Florida.
During the five-week summer recess, Obamacare has been riling up constituents at town hall-style meeting in lawmakers' home districts, with both critics and supporters airing their views.
Republican Representative Tim Huelskamp of Kansas told Reuters there was a "large divide between Republican leaders in (Washington) D.C. and Republicans in the rest of the country."
Huelskamp, who participated in the call and agrees with using the government shutdown strategy on Obamacare, said Republican leaders were ignoring that divide "at their own peril."
Republican leaders have been working to find alternative ways 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 measure.
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.