The Senate Finance Committee will perpetrate a huge fraud on the US public today. Chairman Max Baucus promises to hold a final vote on his health-care overhaul — most of whose costs he has hidden with budgetary gimmicks.

The widely reported numbers are wrong: This bill would increase the deficit and cost more than $2 trillion over 10 years.

Yes, the headlines on the Congressional Budget Office’s preliminary cost estimate were that the bill could cost $829 billion over 10 years and trim the federal deficit by $81 billion. But those numbers are pure fantasy — as CBO plainly, if gently, indicated.

First off, Baucus relies on some cuts that we know won’t actually get made.

Long ago, Congress enacted a series of annual cuts to Medicare physician payments that were supposed to begin in 2003. Starting that very year, however, Congress has repeatedly blocked those cuts.

Yet Baucus — contrary to all experience — assumes Congress will let those cuts take place starting in 2012. That implausible assumption creates some $234 billion in “savings” that will never materialize. Factor them out, and the supposed $81 billion in deficit reduction becomes $153 billion in fresh deficit spending.

The CBO’s language pooh-poohing Baucus on this was pure bureaucratese — but the agency essentially told Baucus: If the sun rises in the west from 2012 through 2019, then yes, this bill would reduce the deficit.

What of that $829 billion cost figure? It’s only CBO’s estimate of new federal spending on expanded insurance coverage. On his blog, ex-CBO Director Donald Marron suggests that the bill’s other new spending on health-related items boosts the total to $904 billion.

Plus, Baucus mandates new state spending on Medicaid — $33 billion, the CBO estimates. New total: $937 billion.

But Baucus’ most audacious gimmick is to push half the cost off the federal budget and onto the private sector — while persuading the CBO to ignore those costs.

The Baucus bill, like every other bill Congress has produced and the overhaul recently enacted in Massachusetts, would expand coverage by forcing Americans to buy insurance. Maybe you don’t want to call it a tax, but it’s still plainly a cost.

How large a cost? The Massachusetts Taxpayers Foundation found that new federal and state spending accounts for just 40 percent of the Bay State’s reforms’ cost — and the private-sector mandates for 60 percent.

Apply that ratio to the Baucus bill, and its actual cost exceeds $2 trillion.

In 1994, the CBO effectively killed the Clinton health plan by counting its private-sector mandates as part of the cost. This time around, congressional leaders wrote their bills so that CBO wouldn’t count them. But it’s just a gimmick — the mandates are still part of this bill’s cost.

Baucus & Co. have done a good job of fooling most people about the cost of their legislation. But as Abraham Lincoln admonished, that only works some of the time.

The CBO’s formal “score” of the bill should include a cost estimate of the private-sector mandates. Then we can debate the full scope of the legislation and not just the parts Sen. Baucus wants us to see.