The Senate immigration bill will be a major boost to the federal budget but does relatively little to clamp down on illegal immigration — cutting the future flow by only about 25 percent — according to the Congressional Budget Office analysis of the bill, released Tuesday afternoon.

Under the bill, which legalizes illegal immigrants and invites in foreign workers, immigration will total 10.4 million more people over the next decade and 16.2 million by 2033.

Those findings will give ammunition to both supporters and opponents of the bill, which the Senate is debating.

On one hand, the boost in federal revenue over the next decade, which the CBO said will total $197 billion, will help quell concerns that taxpayers will be stuck with a large bill. But the CBO’s estimate that the bill solves only about a quarter of the illegal immigration problem will undercut the sponsors’ claims that they are serious about border security and interior enforcement.

The CBO said the bill does include stiffer enforcement and workplace checks, which will make a dent in illegal immigration. But the nonpartisan agency said it expects many guest workers will refuse to go home when their time is up, meaning that illegal immigration will continue.

“Other aspects of the bill would probably increase the number of unauthorized residents — in particular, people overstaying their visas issued under the new programs for temporary workers,” the agency said. “CBO estimates that, under the bill, the net annual flow of unauthorized residents would decrease by about 25 percent relative to what would occur under current law.”

That works out to about 1.6 million fewer people in the U.S. in 2023 than would otherwise come, and about 2.5 million fewer people by 2033.

About 7.7 million current illegal immigrants will have obtained legal status by 2018, the CBO said. Current estimates say there are about 11.5 million illegal immigrants in the U.S., but not all of them arrived early enough to qualify for the bill’s legalization and some others won’t seek legal status.

As bruising as the illegal immigration numbers were, the financial figures were encouraging for the bill’s backers.

The CBO said legalizing illegal immigrants and bringing in workers will cost $262 billion in new tax credits and other spending, but that’s more than covered by the $459 billion in higher taxes paid by newly legalized illegal immigrants and future workers.

For the period from 2023 to 2033, the CBO said, the government would save about $700 billion more, for a total 20-year savings of nearly $900 billion.

“Simply put, this report is a huge momentum boost for immigration reform,” said Sen. Charles E. Schumer, New York Democrat and one of the eight lawmakers who wrote the bill. “It debunks the idea that immigration reform is anything other than a boon to our economy and robs the bill’s opponents of one of their last remaining arguments.”

The CBO said it couldn’t calculate whether the costs would grow in future decades, when the immigrants who would get legalized under the bill would eventually be eligible for Social Security and other entitlements.

As written, the bill prohibits illegal immigrants from getting most taxpayer benefits for the first decade, so those costs fall outside the CBO’s 10-year window.

CBO analysts did say the bill is written ambiguously so that it’s possible newly legalized immigrants or others would be eligible for food stamps or college aid. The analysts said newly legalized immigrants would likely be able to get unemployment benefits if they lost their jobs and met the criteria of their state’s unemployment program.

The CBO also said that the bill would mean 2.6 million more people will be covered by President Obama’s health care law by 2023, and they will be getting an average of $7,200 in subsidies under the health care “exchanges.” That means the cost of “Obamacare” exchange subsidies rises by $87 billion, the agency said.

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