Updated

Faced with a politically risky push by some Republicans to defund ObamaCare, other party members are turning to an alternative strategy: delay it instead.

Republicans are divided on how to confront the Affordable Care Act. Some, such as Sens. Ted Cruz of Texas and Mike Lee of Utah, are pushing to permanently defund it.

But attaching such a measure to a resolution that funds the government after Oct. 1 runs the risk of a government shutdown if it doesn’t pass. If that happens, Republicans fear they would be blamed.

Former White House chief of staff Karl Rove told Fox News people who overwhelmingly oppose ObamaCare also oppose shutting down the government by a 2-to-1 margin.

"They clearly do not like ObamaCare," Rove said. "They think it’s a failed piece of legislation that is going to hurt the country and hurt their families, but they don’t agree with the strategy of tying it to a defund measure that might lead to a temporary shutdown of the government."

So many Republicans now have a new strategy -- delay the law by a year, especially the individual mandate, just as the president delayed some of its other provisions.

Senate Republican leader Mitch McConnell of Kentucky put it this way: "Doesn't the administration think these folks deserve some relief too? The same kind of delay, at least, that businesses will get? Well, Republicans do."

Republican Rep. Steve Scalise of Louisiana, who will introduce an alternative to ObamaCare Wednesday, said, "the president now has delayed it or says he wants to delay it for big businesses and insurance companies. So American families are now saying what about our relief?"

For Republicans, the key to delay is finding a measure that will win Democratic votes in the Senate.

A measure to delay the law by a year got more than 20 Democratic votes in the House. Sen. Jeff Flake of Arizona said matching the president's other delays might well get votes from Democrats facing tight re-election races next year

"This is gonna be a tough sell in some of those red states that Democrats have to defend anyway,” he said. “So I think it’s quite possible they'll put a lot of pressure on the leadership to go ahead and delay for a year."

"Just think about it," Flake added."Out on the campaign trail, to try to justify why the law is being delayed for businesses but not individuals."

Others argue that Democratic votes for delay could change the political equation for the president.

"If the narrative changes from simply Republicans versus Democrats," Rove said,"to Republicans and Democrats versus President Obama, that is a better narrative for Republicans."

A one-year delay would even satisfy, at least temporarily, some of those behind the permanent movement to defund.

"A year’s worth of delay in ObamaCare would be better than letting ObamaCare kick in as planned right now," Lee said.

"Look, anything that delays or stopsObamaCare is a good thing,” Cruz added. “Because ObamaCare is the number one job killer in this country."

As the date nears for a decision, a new Fox News poll showed that ObamaCare remains deeply unpopular with Americans: a whopping 68 percent of those surveyed said they were concerned about their care under new law while only 31 percent were not worried.

Even 56 percent of Democrats expressed concern, with 31 percent saying they were "very" concerned.