The short answer is NO.
For federal elections, there is NO link between the election and taxation. Federal elections include elections for President and Vice President, the U.S. Senate and the U.S. House of Representatives. An easy distinction is this: If you're voting to send the candidate to Washington, DC, it's a federal election.
Do NOT confuse your eligibility to vote in federal elections with your eligibility to vote in state and local elections. If you vote for federal offices only, the act of voting will have no effect on your liability to pay state income tax or any other tax. If you vote for state or local offices, under state law, the act of voting could conceivably be used to establish your domicile and therefore your liability to pay the state income tax.
The U.S. Government's Federal Voting Assistance Program states:
Voting in an election for Federal offices only may not be used as the sole basis to determine residency for the purposes of imposing state and local taxes. If you claim a particular state as your residence and have other ties with that state in addition to voting, then you may be liable for state and local taxation, depending upon that particular state law. Consult your legal counsel for specific questions or situations.