CNN — After members of Congress return from their monthlong recess, Washington will brace for yet another budget battle that entails reaching an agreement to continue funding the government beyond September 30.
The debate will probably center on whether Republicans should attach a measure to defund Obamacare to the upcoming spending bill. But Democrats and some Republicans argued Sunday morning that taking such an approach will almost guarantee more gridlock in Congress.
Rep. Steve Israel, D-New York, for example, predicted on CNN's "State of the Union" that Republicans would come back in September and "double down on obstruction."
"The fact of the matter is that their chaos, their extremism is hurting the economy," said Israel, chairman of the Democratic Congressional Campaign Committee. "We should pass a budget in September instead of shutting down the government."
Several conservative senators - including Marco Rubio of Florida, Ted Cruz of Texas and Rand Paul of Kentucky - have largely given voice to the threat of a government shutdown. And a bloc of about 71 House Republicans say they will refuse to vote for a measure that funds the government if it continues to fund the Affordable Care Act.
The legislative maneuver would add to the 40 times that the House has already voted to get rid of the president's signature health care reform, which Republicans say will damage the economy.
Cruz said Monday that Washington's top priority should be restoring economic growth.
"And nothing is hurting economic growth more than Obamacare," he told CNN's Jake Tapper on "The Lead."
But not all GOP lawmakers are signing on to the shutdown strategy. Sen. Saxby Chambliss of Georgia said Sunday that Cruz's approach is "playing into the hands of the president politically and not the right thing to do."
"Plus, it's going to do great harm to the American people if we pursue that course," he added.
Alex Castellanos, a Republican strategist and CNN contributor, said Republicans "have never been very good at playing 'the shut down the government card.'
"It has actually never helped. 'We're going to hold our breath, until you, the voter, turns blue,' is not good political strategy," he told Candy Crowley, CNN's chief political correspondent.
Asked in a "Fox News Sunday" interview if he supported the short-term extension, House Majority Leader Eric Cantor said "yes."
"I think most conservatives - most on the left, Republicans, Democrats alike - say we shouldn't be for a government shutdown," he said. He added, however, that House Republicans are trying to "fund the government and make sure also that we take away the kinds of things that are standing in the way of a growing economy, a better health care."
Rep. Paul Ryan, R-Wisconsin, chairman of the House Budget Committee, said trying to defund Obamacare by tying it to the continuing resolution isn't as simple as it appears.
"With the government shutdown, we're talking about discretionary spending, government agency budgets. But it doesn't affect entitlements. Obamacare is an entitlement like Medicare and Social Security is, so the entitlement continues on, even under a government shutdown scenario. So it's just not that simple and easy," he said on CBS' "Face the Nation."
Paul said all Republicans want to see Obamacare eliminated, but he cautioned there are better strategies than trying to defund it come September 30.
"Rather than swinging for the fences and trying to take this entire law out with discretionary spending, I think there are more effective ways of achieving that goal," he said. "We think that we can do better by delaying this law."
Rep. Tom Cole, R-Oklahoma, Sen. Richard Burr, R-North Carolina, and Sen. Tom Coburn, R-Oklahoma, have also publicly opposed the shutdown threat.
And while House Speaker John Boehner isn't overtly ruling out picking a fight with President Barack Obama over a spending bill, he is laying out an alternative strategy to avoid a government shutdown. During a closed-door meeting Wednesday with House Republicans, Boehner tried to "gently hold members' hands and walk them away from this," said one GOP source who was in the room.
CNN senior congressional producer Deirdre Walsh contributed to this report.