Today, the Congressional Budget Office released a report saying the Senate's comprehensive immigration reform bill would reduce the federal budget deficit by $200 billion over the next ten years and $690 billion over the following ten.

This chart shows how those numbers add up. Additional spending is above the line, and added revenues are below it:

immigration reform deficit impactBusiness Insider, data from Congressional Budget Office

An increase in immigration will grow federal spending. Almost all of the spending increase will be in two areas: low-income health programs like Medicaid; and refundable tax credits, like the Earned Income Tax Credit and the Child Credit.

But those spending increases will be more than offset by increases in tax receipts, due to two factors. The total population will rise, meaning more workers and more taxpayers. And immigrants will be more likely to be working on the books and paying the taxes they owe.

All told, that means an extra $2 trillion in tax receipts over the following decade. Once you net $1.1 trillion in added spending, that should reduce deficits by $900 billion, or 0.2% of GDP over the next 20 years — not a fiscal sea change, but not trivial either.

The CBO report may actually understate the deficit reduction due to immigration reform. Normally, CBO evaluates legislation on a "static" basis, meaning they don't account for economic changes spurred by policy change. Here, they relaxed that practice to account for the rise in population that the bill would cause. They still did not account for broader economic benefits that immigration reform might produce, such as an increase in productivity or innovation.

One of the main rationales for immigration reform is that it will make the American economy not just bigger but more productive. If that's true, then its positive effects on GDP, and therefore the federal budget deficit, should be even better than CBO estimates.