What can Congress do to stop Obama's immigration plan? Not much.

Exercise the power of the purse! That’s been the battle cry from some Republicans in Congress who strenuously oppose President Obama’s executive order granting temporary deportation relief to millions of illegal immigrants.

They want Congress to exercise its authority over the budget-making process to starve Mr. Obama's new directive of funding.

But guess what? In this particular instance, it turns out there is no power of the purse.

That's because the primary agency that would carry out the president’s anticipated order is funded by fees collected from applications – not by funds appropriated by Congress, Jennifer Hing, spokeswoman for the GOP-controlled House Appropriations Committee explained to reporters on Thursday.

So Congress has no power to block – or rescind – these funds.

Congress, she says, appropriates “zero” funds for the Citizenship and Immigration Services (CIS) agency. “We don’t fund their building. We don’t fund their salaries and expenses. We don’t fund anything related to CIS.”

Which leaves Republicans – who are lambasting the president for skirting Congress and acting like “an emperor” – searching for other strategies, even as the GOP leadership in both houses is greatly discouraging any talk of a government shutdown or impeachment.

One option is to take advantage of where Congress is in the budget process. Before it broke for the elections, Congress passed a short-term budget continuation that expires on Dec. 11. Instead of passing an “omnibus” bill that funds the government through the rest of the fiscal year (through Sept. 30), some conservatives favor passing another short-term spending bill. That way, the final budget decisions would be made in the next Congress, which will be completely controlled by the GOP.

But the problem that exists now with the Citizenship and Immigration Services will exist in the new year. There are no funds to block.

“Later on, if we find out down the road that other agencies have some piece of it, then we can go back and look specifically at those agencies,” says Ms. Hing.

One idea among conservatives now is to fund most of the budget through the end of the year, but separating out immigration-related agencies into a short-term bill.

Potentially, Republicans could decide to withhold funds for CIS’s parent agency – the Department of Homeland Security – but would they really want to hold hostage the agency that’s supposed to protect the country from terrorism?

“There’s nothing we can do to stop an inaction,” lamented Rep. Pat Tiberi (R) of Ohio to reporters on Thursday. The president is saying the administration is not going to do anything with millions of people, he explained. “It doesn’t really require any money to not do anything.”

And so Republicans will have to consider other leverage points that potentially have nothing to do with the focus of the president’s executive order, Congressman Tiberi said. Things like blocking all presidential nominees, except those related to national security – an idea favored by Sen. Ted Cruz (R) of Texas.

“Make no mistake, make no mistake, when the newly elected representatives of the people take their seats, they will act,” warned Sen. Mitch McConnell (R) of Kentucky – the incoming Senate majority leader – from the floor of the Senate on Thursday.

But what exactly will they do?

The Republican leadership isn’t saying yet. Said Senator McConnell: “We’re considering a variety of options."