No 1099 doesn't mean tax-exempt
A low-income taxpayer who babysits, mows lawns, or delivers newspapers is required to report that income, whether or not it is reported on a 1099-MISC or W-2. The same is true for Senator Daschle.
The IRS provides further guidance here (boldface emphasis is mine)
What is Taxable?
Taxpayers must report all income from any source and any country unless it is explicitly exempt under the U.S. tax code. There may be taxable income from certain transactions even if no money changes hands.
Generally, the IRS considers all income received in the form of money, property or services to be taxable income unless the law specifically provides an exemption. This document discusses a few types of reportable income. Information on how to report other types of income can be found in Publication 525, Taxable and Nontaxable Income.
The IRS also covers the topic of taxable and nontaxable income in Tab D of your Pub 4012 Volunteer Resource Guide, page D-1.
As Iowa CPA Joe Kristan notes:
Small businesses get audited every day on personal use of cars. Most businesses are painfully aware that there are at least tax issues involved in personal use of vehicles; how can a Senator who writes the tax laws miss the boat? And failing to report $80,000 of cash? How do you miss that? You aren't surprised to hear the "no 1099, no taxes" excuse from somebody who takes cash on the side for odd jobs, but from a former Senator? Especially a former Senator who threw lots of stones from his glass house.
As bad as these tax problems are, they highlight a worse scandal: how Senators like Mr. Daschle and Iowa's Tom Harkin become millionaires on their $174,000 Senate salaries via their wives' "lobbying" jobs. When Rod Blagojovich pointed out that a Senate seat is "a ... valuable thing," he knew what he was talking about.
Ironically, at least one of Mr. Daschle's clients was a large health insurer, from an industry which benefits greatly from the current tax treatment of employer-provided health insurance--as well as Medicare contracts that Mr. Daschle would oversee if confirmed as Secretary of HHS.