Ever heard of the “tax gap”? It’s the difference between what all of us owe the federal government in taxes each year – and how much, due to errors or cheating, the government actually collects.

Sen. Max Baucus, D-Mont., chairman of the Senate Finance Committee, has long sought to reduce the tax gap, estimated at $350 billion annually. And, working with Sen. Charles Grassley, R-Iowa, the senior Republican on the committee, it seems he has finally succeeded – by vetting the elites nominated by President Barack Obama for positions in his administration.

The size of the gap is debatable. But no one disputes that it’s a significant amount, that policymakers should seek to close it, and that the surest way (until now, at least) to whittle it down is to simplify the tax code. It’s important to assure those who do pay their full share under the law that others are doing likewise. It’s especially important that American taxpayers are confident their political leaders are paying their fair share. Which brings us to President Obama’s nominees. He put forward Tim Geithner to be Treasury Secretary, and Geithner suddenly paid $34,000 of tax owed from previous years. One hopes his tax check cleared the IRS before he was sworn in to head the department responsible for the IRS.

Then along comes former Democratic Senate Majority Leader Tom Daschle.

Obama nominated Daschle to serve as secretary of the Department of Health and Human Services and as the nation’s “health policy czar.” Surprise, surprise: Faced with the thorough vetting process of the Baucus-Grassley Senate Finance Committee, Daschle, it turns out, failed to pay $140,000 in taxes for work since he left the Senate.

Daschle made a big mistake, and he paid for it – not just in taxes and penalties, but in having to withdraw from consideration for his dream job. And he’s not the only nominee to crash in tax flames. The same day, Nancy Killefer had to withdraw as a high-profile nominee to be Chief Performance Office at the Office of Management and Budget over a still-undisclosed tax gaffe relating to payroll taxes on her household help.

Obama’s tendency to nominate reformed tax cheats sends a disturbing signal to taxpayers – one that’s likely to have a corrosive influence on tax compliance. As a political matter, it affirms a common perception that liberals are prone to a “do as I say, not as I do” mentality.

Yet something good can come of this. These nominations have shown that we can make significant inroads on the tax gap. All we need to do is greatly expand the ranks of administration appointees subject to Senate Finance Committee vetting.

Think of how the tax gap will shrink as this serial vetting goes forward, as all the higher-tax elites who hope for Obama administration appointments hurriedly pay the taxes they forgot to pay – and scrupulously pay their future taxes. We could be sitting on a tax-gap closing gold mine.

J.D. Foster is the Norman B. Ture Senior Fellow in the Economics of Fiscal Policy at The Heritage Foundation.