Just for clarification the highest marginal tax bracket in the US is 35%.  That means that on the last dollar of TAXABLE income, a rich individual (>$388,350 for single filing status) is able to keep 65 cents of that dollar, the government takes 35 cents, not 70.
However, most of the rich people you probably have in mind make most of their money from capital gains (ie. investments).  Long-Term (>1 year) capital gains are taxed at a preferential rate of 15%.
So no, the government does not keep anywhere near 70 cents per dollar.
Also, if a person falls in the 35% tax bracket, they do not pay 35% on every dollar they earn.  They pay 35% on every dollar they earn above $388,350.  So whoever said a person who makes $1 million pays $350,000 in taxes, no they don't.  The calculation for how much tax a person with $1 million dollars of ORDINARY income would pay is:
$1,000,000   - Gross Income
($5,950)        - Standard Deduction (varies for filing status and if you are able to itemize, this is single)
($3,800)        - Personal Exemption (varies for amount of dependents, this is one (yourself))
___________
$990,250      - Taxable Income
Total Tax:
$870             - 10% Tax Bracket
$3,998          - 15% Tax Bracket
$12,575        - 25% Tax Bracket
$26,040        - 28% Tax Bracket
$69,201        - 33% Tax Bracket
$210,665      - 35% Tax Bracket
= $323,349 Total Tax
= 32% Effective Tax Rate with a 35% Marginal Tax Rate
HOWEVER, if all of the $1 million dollars was from long-term capital gains they would pay $148,536, or an effective tax rate of 14.9%.
/end tax lesson
*This is an overly simplified example for illustrative purposes.  $323,349 is the MOST tax a person with $1 million dollars of income would end up paying.  Most people with this kind of income are itemizing deductions to reduce their taxable income below $990,250.
** This is all based on 2012 tax law.  Rates are scheduled to go up in 2013 if there is not further legislation.