First, no, the rebate checks will not be taken out of the refund amount you receive in 2008. This is a misconception that probably stems from a CNN article that, earlier today, erroneously implied that the rebates would be borrowed from next year's tax returns. The article has since been revised.
The bill works by reducing the tax code's 10 percent bracket on the first $6,000 of taxable income to zero for 2008. That 10 percent of the first $6,000, $600, will come back to you as a check in advance, probably sometime in May. That check will basically be a "prebate" on a temporary tax cut that will be enacted next year. So, since the new zero percent tax on the first $6,000 of your income will have already been taken care of, when you go to file your taxes in 2008, everything will seem normal and you will be eligible for the same refund amount as always. The rest of your income will be taxed as usual.
Note that, even though the rebates will be worked into the tax code for 2008, eligibility will be based on 2007 income levels. As long as your income is $3,000 or above in 2007, you are eligible for a rebate of at least $300.
This brings us to the second question -- whether you will have to pay taxes on the rebate checks as if they were regular income. Again, the answer is "no." Since the rebate checks are simply advances on a future expansion of how much of your income is tax-free, they are essentially federal tax refunds and won't be considered "income." Since federal tax refunds are not deductible, they are never treated as taxable income.