* Republicans aim to withhold funds from healthcare reforms
* Rubio calls law "this terrible mistake"
* Democrats pledge to fight rollback
By David Lawder
WASHINGTON, July 18 (Reuters) - Growing numbers of Republicans in Congress are setting their sights on a new target in looming fiscal showdowns this autumn over government funding and the debt limit: "Obamacare."
Several Republicans are pledging to oppose a stopgap government spending bill that will be needed by Oct. 1 unless it withholds funds from the implementation of President Barack Obama's signature healthcare law - especially its core requirement that uninsured Americans obtain health coverage.
Blockage of the funding measure could lead to a shutdown of government agencies, roiling financial markets.
The effort to use the budget to undermine the healthcare law, which has been dubbed Obamacare, comes during a new Republican assault on the law after a recent decision by the White House to delay for a year a key requirement that larger employers offer health coverage.
The Obama administration is pressing ahead with the individual mandate, and the Oct. 1 launch of online health insurance exchanges is adding to the anxiety.
Obama on Thursday touted benefits that Americans were already receiving from the law, including some $500 million in rebates to employers and individuals paid by insurance companies .
"I recognize that there are a lot of folks in this town at least, who are rooting for this law to fail," Obama told a White House event. "What I've heard is just the same old song and dance. We're just going to blow through that stuff."
Republicans who control the House of Representative have attempted 39 times to repeal or undermine the Affordable Care Act since its passage in 2010, arguing that it will cost jobs, reduce employee working hours and raise health insurance costs.
They made another run on Wednesday, voting to delay the individual coverage mandate, but the symbolic effort faces virtually certain death in the Democratic-controlled Senate.
On Thursday, Republican Senator Marco Rubio implored his Senate colleagues to use the widely expected short-term spending bill, known as a continuing resolution, to "put the brakes on this terrible mistake."
"Don't come here and say, 'I'm against Obamacare' if you're willing to vote for a budget that funds it. If you pay for it, you own it," said Rubio, who was elected in Florida in 2010 during a wave of negative sentiment toward the health reforms.
A fellow Tea Party Republican, Senator Ted Cruz of Texas, also capitalized on the latest flare-up of Republican anger at the healthcare reforms by introducing legislation to defund them permanently. He will likely seek to move the measure as an amendment to the funding bill.
Although Senate Minority Leader Mitch McConnell is one of 17 co-sponsors for Cruz's bill, he has not weighed in on the specific merits of holding hostage government agencies or the debt limit increase over healthcare funding.
"Republicans will absolutely have a discussion about defunding Obamacare this fall. They are still discussing how to go about that," said a senior Senate Republican aide.
In the House, there is little consensus among Republicans over what to demand from Obama and his Democrats in exchange for a short-term funding bill and an increase in the $16.7 trillion debt limit, which will likely be needed in November.
While much of the discussion has surrounded tax reform and cuts to the Medicare and Social Security benefits programs for the elderly, Obamacare funding is quickly gaining prominence in the list of demands.
"There's a growing group in the House that is retraining its focus to Obamacare," said Representative Mick Mulvaney, a conservative Republican from South Carolina.
"It is completely appropriate to use the debt ceiling or the CR to ask for some changes that reduce the burdens of this law on Americans," he said.
Representative Steny Hoyer, the No. 2 Democrat in the House, vowed to fight efforts by Republicans to stall Obamacare, saying: "Health reform is working. It is the law of our land, an Democrats will continue to make sure that the clock is not turned back."