No, you pay income tax on all amounts of income, even $1. The $600 threshold you are referring to refers to requirements for issuing tax forms. For example, a lender doesn't have to actually issue (mail to you) a Form 1098 unless the interest is over $600. Likewise, if you are an employer and have an independent contractor (Form 1099MISC), you don't have to issue the form to the contractor unless it is over $600. But, this doesn't mean you don't have to pay tax on this amount. You still need to report and pay income tax on all amounts.
Of course, because of deductions and exemptions, if that is your only amount of income, then you would not pay tax on it. For example, a single person under 65 not being claimed as a dependent would not begin to pay income tax until after $10,350 in income because of the standard deduction and personal exemption.