Automated presidential primary phone calls are legal under Federal and New Hampshire state laws

Federal law:

If I register my number on the National Do Not Call Registry, will it stop all telemarketing calls?

No. Placing your number on the National Do Not Call Registry will stop most telemarketing calls, but not all. Because of limitations in the jurisdiction of the FTC and FCC, calls from or on behalf of political organizations, charities, and telephone surveyors would still be permitted, as would calls from companies with which you have an existing business relationship, or those to whom you’ve provided express agreement in writing to receive their calls.

Are calls from political organizations or calls soliciting for charities covered?

Political solicitations are not covered by the TSR at all, since they are not included in its definition of “telemarketing.” Charities are not covered by the requirements of the national registry. However, if a third-party telemarketer is calling on behalf of a charity, a consumer may ask not to receive any more calls from, or on behalf of, that specific charity. If a third-party telemarketer calls again on behalf of that charity, the telemarketer may be subject to a fine of up to $11,000.

Source: http://www.ftc.gov/bcp/edu/pubs/consumer/alerts/alt107.shtm

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New Hampshire state law:

CHAPTER 664: POLITICAL EXPENDITURES AND CONTRIBUTIONS

664:1 Applicability of Chapter. The provisions of this chapter shall apply to all state primary, general and special elections, but shall not apply to presidential preference primaries. The provisions relating to political advertising, RSA 664:14 through 17-a, shall additionally apply to city, town, school district and village district elections. The provisions relating to voluntary expenditure limitations, RSA 664:5-a and 664:5-b, shall additionally apply to elections for United States senator and representative to Congress.

<...>

RSA 664:14-a Prerecorded Political Messages. I. In this section, “prerecorded political message” means a prerecorded audio message delivered by telephone by:
(a) A candidate or political committee; or
(b) Any person when the content of the message expressly or implicitly advocates the success or defeat of any party, measure, or person at any election, or contains information about any candidate or party.
II. No person shall deliver or knowingly cause to be delivered a prerecorded political message unless the message contains , or a live operator provides, within the first 30 seconds of the message, the following information:
(a) The name of the candidate or of any organization or organizations the person is calling on behalf of.
(b) The name of the person or organization paying for the delivery of the message and the name of the fiscal agent, if applicable.
III. No person shall deliver or knowingly cause to be delivered a prerecorded political message to any telephone number on any federal do not call list.
IV. (a) A violation of this section shall result in a civil penalty of $5,000 per violation.
(b) Any person injured by another’s violation of this section may bring an action for damages <... rest deleted 'cause it's long>

Source: http://www.sos.nh.gov/rsa664.htm

Section 664:14-a seems to be causing some confusion because it says it's illegal to call numbers on the Federal Do Not Call Registry, but the heading above clearly states that none of the provisions of Chapter 664 apply to Presidential primaries.

These calls are legal under federal and state law.