In Congress’ standoff over immigration policy, Republicans seem to be battling not only President Barack Obama but their own rhetoric on government spending.

Immigration riders attached to the Homeland Security spending bill by the House GOP turn out to actually widen the budget deficit over the next 10 years, according to the Congressional Budget Office. As a result, the $39.7 billion measure will need a supermajority of 60 votes under Senate budget rules, even if Republicans get past the Democratic filibuster.

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Faced with a Feb. 27 deadline and the Presidents Day recess next week, time is short. And the CBO report never addressed an added cost implicit in the Republican position: How much would it cost for the government to deport all the undocumented workers who stand to benefit from Obama’s most recent executive order?

That could be upward of $20 billion to $25 billion, according to the best estimates collected by POLITICO.

It’s a sum hard to find these days, given the Republican-backed spending caps imposed on the House and Senate appropriations committees. Indeed, just last week, the GOP leadership ridiculed Obama’s proposal to amend the law to increase discretionary funding — including money for DHS — above the freeze set for fiscal 2016.

The president’s critics on immigration, like Sen. Jeff Sessions, argue that the fight is not about dollars but the will to enforce the law. “Has the Obama administration ever asked for the resources necessary for the task of enforcing the law? Of course not,” said a spokesman for the Alabama Republican.

But what’s most striking is how each side has invoked Congress’ power of the purse to bolster its arguments in the immigration fight.

Republicans are employing their constitutional power to deny funding to the executive agencies that would carry out the president’s November order, as well as a 2012 order which deferred deportations for young undocumented immigrants. But Obama essentially makes the same argument in reverse to justify himself: He says Congress left him with this discretion precisely because it failed to give him the money to fully enforce the immigration laws.

“The proposed policy is designed to respond to the practical reality that the number of aliens who are removable under the [Immigration and Naturalization Act] vastly exceeds the resources Congress has made available to DHS for processing and carrying out removals,” reads the 33-page opinion from the Justice Department’s Office of Legal Counsel. “The resource constraints are striking. … DHS has informed us that there are approximately 11.3 million undocumented aliens in the country but that Congress has appropriated sufficient resources…to remove fewer than 400,000 aliens each year, a significant percentage of whom are typically encountered at or near the border rather than in the interior of the country.”

For all the political stakes, it’s surprisingly difficult to get an estimate of how much it costs the government to deport an individual. But money appears to make a difference. Tables compiled by DHS show that the number of annual removals has risen more than 80 percent in the past decade, while enforcement and detention appropriations have doubled in inflation-adjusted dollars.

POLITICO published its own calculations in November after comparing 10 years of appropriations with the number of annual removals listed by DHS. There were spikes and dips along the way, but the results showed a relatively consistent pattern of about $7,200 — plus or minus $1,000 — for each removal.

When shown these numbers, DHS’s Immigration and Customs Enforcement came back with its own estimate that the agency’s average “life cycle” cost for each removal it completed in fiscal 2013 was about $8,661.

Jennifer Elzea, a spokeswoman for ICE, explained that the agency “does not track the average cost of removal for an alien, but rather the average life cycle cost per alien. … This cost is inclusive of the Immigration Enforcement Lifecycle including all costs necessary to identify, apprehend, detain, process through immigration court, and remove an alien.”

If the government greatly ramped up the number of deportations, that figure might come down. Then again, that number may understate the full costs since the immigrant population affected by Obama’s order is relatively difficult for ICE to identify: individuals who have lived peacefully in the U.S. interior for years and become part of their communities.

But taken together, the numbers from POLITICO and ICE indicate that removing 3 million immigrants could cost the government between $20 billion and $25 billion.

Immigration rights advocates say 3 million is roughly how many people could seek temporary work permits under Obama’s November order, out of a total eligible population pegged at more than 4 million.

CBO’s analysis is more cautious and assumes that just 1.5 million adults will have come forward and been approved as of 2017, the year Obama’s presidency ends.

Since the House amendments seek to overturn Obama’s 2012 order as well, CBO adds about 750,000 young people who have already been granted temporary status or will become eligible by 2017. The total then is about 2.25 million people affected by the House amendments. And in estimating future Medicaid and education costs, CBO factors in the likelihood that more children will be born in these families and qualify for assistance.

In truth, Obama is doing more than simply deferring deportations for lack of resources from Congress. His November order establishes a process for individuals to get temporary work permits and qualify for government benefits — going well beyond deciding who gets prosecuted and who does not.

The Justice memo concedes as much. It says: “The conferral of deferred action does not represent a decision not to prosecute an individual for past unlawful conduct; it instead represents a decision to openly tolerate an undocumented alien’s continued presence in the United States for a fixed period.

“This difference is not, in our view, insignificant,” the memo adds. “But neither does it fundamentally transform deferred action into something other than an exercise in enforcement discretion.”

But the key word is “tolerate.” Led by Texas, 26 states are hitting hard on this same point in a lawsuit challenging Obama before a federal judge in Brownsville. Sessions’ office argues too that CBO fails to count the added costs that Obama’s order will impose on state and local governments.

At the federal level, CBO estimates that two-thirds of the increased government outlays stemming from Obama’s executive orders would consist of cash payments under the Earned Income Tax Credit. As of now, the migrants don’t qualify because the EITC is not available to low-income workers who lack Social Security numbers.

The House-passed amendments, by overturning Obama, would save the government a total of $14.85 billion from 2015 to 2025, CBO says, of which an estimated $10.25 billion is from the increased earned-income credit payments. Other costs include nutrition and health-care benefits.

Whatever the outcome of the current debate, Sen. Charles Grassley (R-Iowa) hopes to trim the EITC payments with legislation prohibiting the protected workers from applying retroactively for earned-income credits once they obtain Social Security numbers.

The Internal Revenue Service typically allows taxpayers to amend their past filings for the three prior years after getting a Social Security number. But Grassley argues that this ought not to apply here since the earned-income credit is meant to encourage work, which in this case was illegal employment prior to Obama’s order.

Early estimates by the Joint Tax Committee indicate that up to $1.7 billion could potentially be saved if Grassley makes this change.

Yet the same coin has another side: All these calculations show that this is a migrant population that is working — albeit in low-paying jobs — and generating substantial payroll taxes that would only grow under Obama’s plan.

This pattern has been seen before in disputes over child tax credits going to migrants who are not required to have Social Security cards. In 2010, for example, Treasury inspectors found that 2.18 million filers with only individual taxpayer identification numbers collected about $4 billion in child credits. But the same workers generated payroll taxes totaling more than $7 billion — more than matching the tax credits’ cost to the government.

In the case of Obama’s executive orders, CBO estimates that $22.3 billion in potential revenues would be lost from 2015 to 2025 if the House amendments were to prevail, including about $17.1 billion at the expense of Social Security. When all the puts-and-takes are counted, the net result is that the deficit would be $7.5 billion wider as a result of the House amendments. [

Obama’s new budget takes this logic a big step further by assuming that more comprehensive immigration reform would translate into $158 billion in deficit reduction over the next 10 years. The numbers draw on CBO’s analysis of the Senate bill adopted in the last Congress and again reflect a 3-to-2 ratio between improved receipts and higher costs.

Conservatives argue that this is illusory, given that the tide will inevitably turn once the newly legalized immigrants reach retirement age. But in Senate testimony last week, Stephen Goss, the chief actuary for the Social Security Administration, said the net cash flow for the trust funds would be positive for 30 years — and that even over 75 years, the cumulative impact of the president’s executive order would be a modest improvement for Social Security.