Op-Ed: How a primary challenge could undo Donald Trump

President Donald Trump 's rocky and freewheeling start to the presidency has led to numerous course-corrections after three months in office. In addition to significant shifts on foreign policy, the seeming death of his health-care bill and the ouster of his National Security Advisor, Trump is sparring with Congress as well as handling his group of bickering advisors.

All of these actions may portend trouble for Trump, but they don't necessarily spell doom for his presidency. Plenty of presidents go through early staff changes and find their sea legs. But for a president who is laser-focused on his re-election run in 2020—to the degree that he filed paperwork for re-election on his inauguration day—Trump should be very concerned. While polls show that many of his voters, including independents, have maintained their support for him, more than any president in memory, Trump has gone after his fellow Republicans, managing to antagonize wide-swaths of his party's faithful.

Trump is clearly mindful of the need to control the GOP. Reports have shown that his political team has been pushing his supporters into positions of control over the individual Republican State Party leaderships, mostly notably winning a battle for the Ohio GOP Chairmanship over Governor John Kasich's choice in the wake of the election. But as Trump has personally proven in his stunning primary run in 2016, that is not enough. Whatever changes Trump has wrought on the political process may make it more likely that a challenger could come after him in 2020.

Trump is right to worry about a challenge. Historically, primary challenges are the death of sitting presidents. Even before the primary and caucus system started taking over the presidential selection process in the early 1970s, incumbents facing any primary challenge find themselves finished by November.

The primary challenge to a sitting president goes back to William Howard Taft's fight with Teddy Roosevelt in 1912. Taft was able to retain the Republican nomination, but he was fatally compromised in the general election, winning only two small states and coming in third in the popular vote.

In 1952, Senator Estes Kefauver ran in the New Hampshire primary and defeated the slate which was scheduled to support Harry Truman. Truman soon announced that he wouldn't run for reelection. A similar, though more dramatic, event happened to Lyndon Johnson in 1968. Johnson's slate nearly lost to Senator Gene McCarthy in New Hampshire and was thought to be badly trailing in Wisconsin when Johnson publicly pulled out of his reelection attempt.

While these three examples happened in the days before the primary system was fully established, presidents faced even greater challenges later on. Gerald Ford barely beat back a Ronald Reagan campaign in 1976 and Jimmy Carter faced down Senator Ted Kennedy's primary race in 1980. Both of the candidates went on to lose in November. So did George H.W. Bush in 1992, as political commentator Patrick Buchanan's populist run, which many see as a precursor to Trump's own campaign, revealed great weaknesses in Bush's campaign strategy.

If any president doesn't have a unified party behind him, that is seen as a major precursor to defeat. Presidents require strong support from the party faithful to win reelection. If what we saw in November holds, Trump can expect that the vast majority of Republicans will have his back in 2020. But if only a small percentage switch or fail to turnout, he can be facing doom. Sitting presidents have to spend their reelection race justifying their decisions to the undecided electorate.

To spend the primary campaign shoring up the base – and making political compromises to the more extreme wings of the party rather than to the independent center – provides more opportunities for an opponent to appeal to the center voters. A strong primary challenge also seems to help engender third party candidates – in 1992, Bush was hurt by Ross Perot's run, and the 1980 race was thrown off by an independent John B. Anderson.

There has already been Republican chattering about possible primary challenges to Trump, with former California Governor and Trump Celebrity Apprentice replacement Arnold Schwarzenegger talking up Kasich in recent weeks.

Trump may not be that worried about Kasich, who he badly defeated in the 2016 primaries, or the other prominent Republicans who went down to defeat in the crowded primary field. But if he continues to stumble, other candidates are likely to start cropping up. The never-Trumpers, such as Nebraska Senator Ben Sasse or Mitt Romney who Trump could have co-opted as Secretary of State but failed to do so, may once again find their voice and may even see an opportunity.

One hundred days into his term, Trump has not managed to stabilize his administration with a string of noteworthy victories. He has plenty of time to right the ship, but if he doesn't, he has something serious to be concerned about. The possibility of a primary challenge is an ever-present threat to any presidential administration.

Commentary by Joshua Spivak, a senior fellow at the Hugh L. Carey Institute for Government Reform at Wagner College in New York. He blogs at The Recall Elections Blog. Follow him on Twitter @recallelections.

For more insight from CNBC contributors, follow @CNBCopinion on Twitter.