Story highlights Some Republicans are pushing to avoid a government shutdown this year

Obama's immigration orders have raised tensions between the President and the GOP

Alternatives to a shutdown include hitting the budget, suing and blocking nominees

When the government shut down last year, Rep. Mo Brooks, R-Alabama, walked up to a fellow conservative a few feet from the House Floor, and high fived him.

Now, Republicans are so shutdown averse, even Brooks tells CNN they should do everything in their power to fight President Barack Obama's immigration executive action. Everything except shutting down the government.

Brooks' change speaks volumes about Republican thinking at a time when the party is weighing a response to Obama's order amid pressure from some influential outside conservative forces are pushing Republicans to go once again down the shutdown route.

"There is no reason to shut down the government over this. It would be bad for the government, bad for the country and playing into his hands in a way," said Sen. Rob Portman, R-Ohio.

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"Nobody wants to shut the government down. I don't know anybody on either side of the aisle with rational thoughts would want to shut the government down. So we start with that premise," echoed Sen. Richard Shelby, R-Alabama.

"I would try anything except a shutdown of the government," added Sen. John McCain, R-Arizona.

The lawmakers spoke in separate hallway interviews.

With a shutdown off the table -- the question is how can Republicans respond? The answer, according to many Republican congressional sources, is that they don't have a lot of viable avenues for beating back the president's executive order, which is expected to allow up to 5 million illegal immigrants to stay legally.

There may not be great options, but there are at least some choices.

Aim for the budget

The first is to use Congress' greatest weapon -- the power of the purse -- without shutting down the government.

A leading idea is to fund the majority of the government for a year, as planned, but carve out funding for immigration-related agencies and only provide money for those for a short time.

One Republican senator, who asked not to be identified in order to speak freely about the strategy, told CNN that such a move would "give us time to come up with a proposal."

"He won't veto either of those, I don't think," the GOP senator said, speaking of the President.

There are pitfalls in this idea -- not the least of which is getting the bill passed in what is still a Democratic-controlled Senate.

But GOP sources admit a broader problem that Republicans have with using the power of the purse to stop the president from enacting his executive action is that Congress doesn't actually fund the immigration agency responsible for enforcement.

U.S. Citizenship and Immigration Services, the primary agency responsible for green cards and work permits, is self-funded -- paid for with customs fees.

That's why other Republican lawmakers admit they would have to put policy riders negating the president's actions on appropriations bills, which would lead back to the short term problem of a government shutdown, since the president is unlikely to sign a bill that rolls back his own executive order.

Another option under discussion is to pass a spending bill in December, but vote separately early next year on a bill that would rescind any funds specifically for those federal agencies that carry out the immigration executive order.

Several Republicans say they could attach this kind of a bill to cancel the money to a one authorizing another program the president supports, which would put him in a tough position to veto it.

Sue the president

Republican lawmakers do believe they will have a good case to take to the courts to fight to the president's actions.

Several House Republicans said a lawsuit should be filed immediately to attempt to halt -- at least temporarily -- the president's plans, but they admit that legal challenge will drag out and should be pursued on a separate track than the debate over government funding.

Some say they that when the new GOP-controlled Congress takes over they will push resolutions formally rejecting and presidential executive order and admonishing him for it. The idea is that showing Congress disapproves will help give lawmakers legal standing in court.

Block the president's nominees

Still another idea floated by some GOP members is to block some of the president's nominations in the Senate in response to executive order. It's unlikely Republicans would refuse to vote on Loretta Lynch, the president's pick to replace Eric Holder as Attorney General, but they could deny votes on other key positions the president want to fill.

CORRECTION: This post has been updated to correct which state Rep. Mo Brooks is from.