Story highlights President Obama is expected to take executive action if Congress doesn't act

Several lawmakers weighed in Sunday saying a shutdown wouldn't solve anything

Mitt Romney says there's "got to be more productive ways" to work with the President

Republican lawmakers overwhelmingly agreed on Sunday talk shows that shutting down the government to avoid unilateral action by President Barack Obama on immigration is not a good option

"I think there's got to be more productive ways for us to be able to impress on the President the need to work for a permanent solution as opposed to a temporary stop-gap solution," Mitt Romney, former Massachusetts governor and two-time presidential candidate, said on the CBS show "Face the Nation."

"The President ought to let the Republican Congress, the Republican House and the Republican Senate, come together with legislation that they put on his desk which relates to immigration. And he can veto it or not, but let the Congress and let this election have its say, as opposed to jumping in by doing something unilaterally -- and in a way which is extraconstitutional -- he's poking an eye of the Republican leaders in Congress, and he's making it more difficult for there to be a permanent solution to this issue."

Another potential 2016 presidential contender for the GOP also weighed in.

"No, we shouldn't shut down the government," Louisiana Gov. Bobby Jindal said on "Fox News Sunday." "But absolutely they should do everything they can to force the President to follow the law."

In September, the White House announced that it would delay any action on immigration until after the November elections. Shortly after the midterms, the President left Washington for a weeklong trip to Asia and Australia. Obama is scheduled to return to Washington on Sunday night, and the issue is expected to be at the top of his agenda.

Photos: Shelter for immigrants Photos: Shelter for immigrants Shelter for immigrants – Immigrants from Central America bow their heads in prayer at a shelter outside Mexico City. Many of them are on their way to the United States. Hide Caption 1 of 8 Photos: Shelter for immigrants Shelter for immigrants – Some nap, while others watch television, at the Casa del Migrante. Residents of the neighborhood have called for the immigrant shelter to close. Hide Caption 2 of 8 Photos: Shelter for immigrants Shelter for immigrants – An immigrant shaves outside the shelter, taking a break after days as a stowaway on a cargo train heading north. Hide Caption 3 of 8 Photos: Shelter for immigrants Shelter for immigrants – Church officials say more than 100 Central American immigrants pass through the Lecheria neighborhood daily. Neighbors called for this shelter housing them to shut down. Hide Caption 4 of 8 Photos: Shelter for immigrants Shelter for immigrants – After long treks in harsh conditions, many immigrants arrive with wounds or infections on their feet. Hide Caption 5 of 8 Photos: Shelter for immigrants Shelter for immigrants – With a well-stocked pantry, cooks prepare warm meals for dozens of Central American immigrants daily. Hide Caption 6 of 8 Photos: Shelter for immigrants Shelter for immigrants – Local church congregations donate clothes for Central American immigrants passing through Mexico. Hide Caption 7 of 8 Photos: Shelter for immigrants Shelter for immigrants – An immigrant couple rests at the shelter, which closed this week after growing conflicts with the neighbors. Hide Caption 8 of 8

Sens.-elect James Lankford of Oklahoma and Tom Cotton of Arkansas both received calls from the President on Election Night, urging compromise on the issue. On Sunday, both resolved not to go down the same path as Sen. Ted Cruz of Texas, who voted to shut down the government in October 2013, less than a year into his first term.

"We're not pursuing a government shutdown," Lankford said on "Fox News Sunday."

"I don't think anyone wants to shut down government because that doesn't solve the problem," Cotton echoed.

A few of their Republican colleagues mirrored their sentiments, with Sen. John Thune of South Dakota saying a shutdown "doesn't solve the problem" and Rep. Tom Cole of Oklahoma saying a shutdown is an "inappropriate weapon (and an) inappropriate tool."

But in rejecting the government shutdown option, Republicans are now faced with a key question: Where must they compromise to pass a bill that the President will actually sign?

Speaking at the G20 Summit in Australia on Sunday morning, Obama outlined his conditions.

"There is a very simple solution to this perception that somehow I'm exercising too much executive authority. Pass a bill I can sign on this issue," Obama said.

"If Congress passes a law that solves our border problems, improves our legal immigration system, and provides a pathway for the 11 million people who are here, working in our kitchens, working in farms, making beds in hotels, everybody knows they're there, we're not going to deport all of them. We'd like to see them being able to be out in the open, pay their taxes, pay a penalty, get right with the law."

Despite vocalizing his aggressive plans for unilateral action on immigration, Obama did concede that any executive action he takes could be undone by his successor.

"The very nature of executive authority means future presidents can reverse those actions," Obama said.

In June 2013, the Senate passed a bipartisan immigration bill that outlined provisions to create a path to citizenship for millions of undocumented residents, while also beefing up security along the border. More than 500 days later, the House has yet to pass a bill of its own, a situation that House Speaker John Boehner insists exists because of the President's unwillingness to compromise.

"We're going to fight the President tooth and nail if he continues down this path," Boehner said at a news conference Friday. "This is the wrong way to govern."