Late last month, Mitt Romney reportedly sat down with Kentucky Sen. Rand Paul for a “productive” half-hour meeting. Naturally, this caused speculation that Romney might choose Ron Paul’s son as his running mate for the fall campaign.

The agenda was probably less ambitious. It’s more likely that Paul wanted to gauge his comfort level for a possible Romney endorsement by discussing policy details. In turn, Romney was reaching out to a prominent Tea Party figure who serves as a bridge between his father’s libertarian-leaning movement and the mainstream of the Republican Party.

But let’s suspend disbelief for a moment and imagine that there’s something to the speculation. What could Romney and the younger Paul intend to accomplish by teaming up? On paper, the match could quiet most remaining conservative discontent with the presumptive nominee. Rand Paul is a rare politician who can still rally the Tea Party after winning office. He also might be the only vice-presidential prospect who could maximize Romney’s share of Ron Paul voters—1.8 million at last count, not including potential Paul sympathizers who were ineligible to participate in GOP primaries—many of whom might otherwise stay home, write in the Good Doctor, or vote third party.

In return, Senator Paul would see his national profile elevated considerably. If the ticket prevailed, he would be vice president of the United States. That would confer upon him automatic frontrunner status for the presidential nomination in 2020. And it would give the libertarian wing of the party a place at the table in a Romney administration. Even if Romney loses, the exposure could help Paul mount a much stronger presidential campaign in 2016.

There are problems with this scenario, however. First, Paul would certainly feature prominently in the Obama campaign’s attacks on Romney for being too right-wing. Indeed, the senator would become Exhibit A. The same can’t be said for less risky choices like Ohio Sen. Rob Portman or Virginia Gov. Bob McDonnell. If Romney is defeated for any reason, expect the conventional wisdom to blame the Tea Party radical under him on the ticket.

In some respects, Paul would be a riskier partner for Romney than Sarah Palin was for John McCain. Barack Obama was in a much stronger position in 2008 and McCain had little chance of winning from the start. Palin was a Hail Mary pass, a last-ditch effort to find a candidate who could rally the conservative base, add both diversity and executive experience to the ticket, and potentially peel off disgruntled Hillary Clinton Democrats. By contrast, Romney is beginning the general election campaign in a dead heat with Obama and has less to gain by making a big splash in the veepstakes.

If Romney-Paul were to win, libertarians and traditional conservatives have to ask: how much influence would a Vice President Paul really have? Dick Cheney presents a distorted picture of the power of the vice presidency. Most vice presidents perform only ceremonial functions, like attending state funerals for foreign dignitaries and casting the occasional tie-breaking vote in the Senate. Despite developing a fairly close personal relationship with Ronald Reagan, George H.W. Bush quipped of his vice-presidential role, “You die, I fly.”

Joe Biden appears to be involved in the White House’s high-level decision-making process (though the extent of his role won’t be clear until after the administration is over). But from what little we know, he seems to be overruled — as he was on both the Afghanistan surge and the bin Laden raid — at least as often as he’s heeded. And foreign-policy expertise is what Biden was supposed to bring to the Democratic ticket.

At best, Paul could end up a vice president on the model of Al Gore: a trusted adviser of the president who is given wide latitude to pursue projects of mutual interest to the vice president and the administration. Alternatively, he could be dispatched to rally the Republican troops like Dan Quayle. Paul would be leaving a Senate seat from which he could check Romney’s interventionist inclinations in foreign policy and centrist tendencies domestically to take a job inside the Romney camp where he could be powerless to shape policy.

If President Romney were to tack to the center at home or wage preventive wars, the only way Vice President Paul could keep his father’s base intact is by resigning. This would be unprecedented. Perhaps a principled resignation over a hypothetical Romney tax increase would even boost Paul’s political fortunes. But if a resignation were motivated by, say, war with Iran, Paul’s departure would doom him in Republican politics and probably not stop the war.

A Romney-Paul unity ticket sounds very compelling in theory. In practice, it would be unlikely to benefit either party.

W. James Antle III is associate editor of The American Spectator and a contributing editor of The American Conservative.