You’re a six-term U.S. Senator suddenly made a Tea Party target and primary underdog, in need of all the votes you can get, not to say that Web-friendly 18-29 demographic. What do you do? Recruit Facebook CEO Mark Zuckerberg to stand next to you on stage, of course.

That’s the strategy of Orrin Hatch, the senior Senator from Utah, who has invited Zuckerberg to appear with him at a technology forum before college students at Brigham Young University on March 25.

The senator, who chairs the Senate Republican High Tech Task Force, will discuss social media and innovation from the economic and public policy perspectives, while Zuckerberg will provide an innovator’s point of view on technology, growth and social media, according to a release announcing the event.

Facing one of the toughest reelection campaigns of his career, Hatch is already moving aggressively to avoid falling victim to the same forces that pushed his longtime Senate colleague, and fellow Republican, Bob Bennett, out of office last year.

The Tea Party movement voted out Bennett at the 2010 state convention, and carried their favored candidate, Republican Mike Lee, to victory in the general election. Lee has said he won’t endorse Hatch in his re-election.

The Party has already named Hatch one of their top 2012 targets, and Rep. Jason Chaffetz (R-Utah) is considering challenging Hatch in the primary.

The joint visit before college students at BYU was instigated by the senator after he met with Zuckerberg in July to discuss public policy and innovation in his capacity as his party’s point-person on high tech issues.

Hatch was first elected to the Senate in 1977, well before the 26-year old Zuckerberg, and likely most of the BYU audience, was even born.

Hatch has Facebook and Twitter accounts, although you probably would not call him the Senate’s “social media genius.” Zuckerberg’s Facebook account, for instance, has around 3.5 million fans, while Hatch has a little more than 5,000.

Hatch and Zuckerberg both, however, have a strong stake in the crossroads of high tech and public policy, and Utah. Atlantic magazine recently placed Utah fifth in its annual survey of the nation’s Top 10 States in science and technology, and major Facebook developer, FamilyLink, is headquartered in the state, along with other online firms like Overstock.com and Ancestry.com.

The forum, free and open to the public, will follow a question-and-answer format.

Questions though must be submitted in advance, through the BYU Facebook page, natch.

Video of the technology forum will later be posted later on the BYU and BYUTV Facebook pages, according to the university.