By Richard Cowan

WASHINGTON (Reuters) - As Republican lawmakers pushed ahead on Monday with a campaign to scuttle President Barack Obama's healthcare program, a survey suggested that they risk a public backlash should their efforts lead to a government shutdown or a default.

The CNBC poll reported that by a 59-19 percent margin, respondents opposed linking defunding of "Obamacare" to a possible shutdown starting on October 1, or to a failure to raise the government's borrowing authority, meaning Washington may not be able to pay all of its bills by sometime in October or early November.

Eighteen percent were undecided, according to nationwide poll of 800 people conducted by Hart-McInturff. It had a margin of error of 3.4 percentage points.

On Friday Republicans in the House of Representatives passed and sent to the Senate a measure that would make continued funding of the government contingent on defunding Obamacare. The bill passed on a mostly partisan vote of 230-189.

They plan a similar strategy when they take up a measure to raise the debt ceiling, which if defeated could lead to a government default.

The Democratic-controlled Senate will take up the House spending bill later on Monday. Democrats expect to send it back to the House by Sunday with the Obamacare provision stripped out, according to a Senate Democratic aide.

That timetable guarantees a down-to-the wire battle through next weekend, with little time for the House to respond to the Senate action.

The long Republican war against "Obamacare" is at the heart of the clashes ahead, just as important provisions of that law start taking effect on October 1.

The only certainty is that when the dust settles, Obamacare will still be standing. Neither the Senate nor the Democratic president will agree to a bill delaying the program, signed into law by Obama in March, 2010, to provide health coverage for millions of uninsured Americans.

LOOKING TO 2014

The clash is a potentially defining moment for Republicans, who are badly divided over the anti-Obamacare tactic being pursued by the House.

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Influential conservatives, including senior Republicans in the Senate, strategist Karl Rove and Fox News broadcaster Bill O'Reilly have called it futile, warning that a shutdown could seriously damage Republicans on the eve of the 2014 mid-term elections.

Congressional authorization for the government to spend money runs out at the end of the fiscal year on September 30.

Senate Majority Leader Harry Reid has made it clear that he will work this week to delete the House Republicans' provision defunding Obamacare.

The first important vote on the House-passed Obamacare spending bill could come by mid-week when Reid might stage a vote on a "motion to proceed," which basically asks the Senate's permission to debate a bill.

Sixty votes in the 100-member Senate likely will be required to approve this procedural move. Democrats control 54 votes -including those of two independents - versus 46 for Republicans.

It was thought that Republicans would surely vote to begin debate on a bill that aims to kill the healthcare law that they hate. But Senator Ted Cruz of Texas could make a filibuster stand at that point, slowing down the process, if nothing else.

TED CRUZ AT CENTER STAGE

Cruz, and to some extent his ally, Senator Mike Lee of Utah, have "gone rogue" on the Republican establishment in the Senate, with Cruz in particular the subject of bitter attack from some of his colleagues for traveling around the country urging a "no surrender" strategy on Obamacare.

If the motion to proceed passes, the Senate would then move to the bill itself with a Democratic amendment to strike the Obamacare provision.

Cruz could try again to slow or block the process by filibustering. Again, 60 votes would be needed move forward.

Winning that second procedural vote would open the door for Reid to then easily destroy the Obamacare provision, leaving the government funding part of the bill alive.

From there, Reid could push to pass the bill, again relying on just the 54 Democratic votes he controls, and then send the bill back to the House.

After the Senate finishes, the measure to fund the government must then return to the House. By then, October 1 will be looming.

DEBT CEILING UP NEXT

House Republicans next week hope to unveil a second important bill - one to prevent the U.S. government from defaulting on its debt sometime in October or November.

The legislation would raise the country's $16.7 trillion borrowing limit. Republicans again want to extract something from Democrats in return for the debt limit hike.

They have been talking about attaching yet another plan to the debt limit bill that would gut or delay portions of Obamacare, as well as forcing approval of the Keystone oil pipeline that would run from Canada to the Gulf of Mexico.

House Republicans say they also are looking at some tax provisions to possibly add onto the debt limit bill.

Obama has warned Republicans against loading up the debt limit bill with unrelated items, saying he will not negotiate on a measure that in effect pays the government's outstanding bills.

Passage of a loaded-up debt limit bill in the House likely would trigger a rerun of the stop-gap spending fight that is consuming Washington now.

The battle over the shutdown and the debt ceiling is to some extent a repeat of fiscal showdowns that have taken up much of the past three years, since Republicans took control of the House in the 2010 elections.

With every one of them, standing of Congress among Americans, never very high, has sunk even lower.

(Reporting By Richard Cowan; Editing by Fred Barbash and Xavier Briand)