According to Karen Hube in the Washington Post, tax cheats reduce federal tax revenues by roughly $350 billion per year. That means we can close about 1/3 of the annual federal deficit with better enforcement, which doesn't require increasing tax rates or reducing deductions and credits. But, even though every dollar invested in IRS enforcment produces $4 in tax revenues, the Republican controlled House of Representatives killed a proposed increase in IRS funding, and unsuccessfully tried to cut funding to the agency.
Common cheats include identify theft using Social Security Numbers stolen from the Social Security Administration Master Death File, overreporting refundable tax credits and underreporting income. In recent years, the IRS has targeted income from overseas.