The Congressional Research Service, a non-partisan arm of Congress, believes that the Congress can, indeed, defund the president's amnesty orders.

Last week, Rep. Hal Rogers, Chair of the Appropriations Committee, said the Congress didn't have to power to defund the U.S. Citizenship and Immigration Services because the agency funded itself through fees.

But the CRS disagreed, saying that the fees still have to be appropriated by statute.

The Hill:

“Importantly, amounts received as fees by federal agencies must still be appropriated by Congress to that agency in order to be available for obligation or expenditure by the agency. In some cases, this appropriation is provided through the annual appropriations process. In other instances, it is an appropriation that has been enacted independently of the annual appropriations process (such as a permanent appropriation in an authorizing act),” the report says.

“In either case, the funds available to the agency through fee collections would be subject to the same potential restrictions imposed by Congress on the use of its appropriations as any other type of appropriated funds.”

Conservative lawmakers, including Sessions, who hope to block or limit the president’s action in an upcoming spending bill, though, insist that House appropriators are wrong. They have called on Congress to block funding from going to the agencies in question. They worry that the immigration actions will be impossible to roll back in the future if Congress does not act now.

Republicans are weighing ways to prevent the immigration action while also avoiding a government shutdown. Lawmakers must pass a spending bill by Dec. 12 to keep the government funded and open. The report will likely embolden conservative critics, including Sessions, who is seeking the Senate Budget Committee gavel.

The Appropriations panel on Wednesday hit back, arguing that the Congressional Research Service study did not undermind its stance.

“In no way does the CRS report contradict anything that we've said. It would take an act of Congress to change the underlying statute to restrict the use of fees,” said an aide to the Appropriations Committee, noting that Congress does not appropriate funds to the agency in question year-to-year.

“To restrict the fees, a law would have to be passed, which means a presidential signature. Barring that, the agency can continue to collect and use fees without an annual appropriation, meaning that in the event of a government shutdown, the agency would continue to operate, while other functions of government close,” the aide added.

Even if Rogers is right, Republicans should still seek to restrict the appropriation by refusing to fund the fees. Force the president to go to court and see what the justices of the Supreme Court have to say about it.

Recission is another option under consideration, although the president could veto any recission bill that defunded his amnesty orders. One way or another, the effort to defund amnesty will come to a head with Obama having veto power over any action the GOP takes.