But in another way, neither of them makes a whole lot of sense for Trump. That's because both men, like Trump, have shown the ability to be broadly disliked — sometimes very disliked.
Before diving in, it's worth noting we do not live in an era of popular politicians, who are usually unknown or disliked. But as in the 2016 campaign, being unpopular can be a matter of degrees, and Christie and Gingrich have been on the low end of that scale in recent years.
Gingrich's popularity has not been tested in national telephone surveys since his unsuccessful campaign for the Republican presidential nomination four years ago. A Washington Post-ABC News poll two months before the primaries found the former House speaker with a narrowly negative image — 35 percent favorable and 42 percent unfavorable. But after months of debates and primary contests — and even questions raised by an ex-wife about whether Gingrich wanted an "open marriage" — Gingrich's favorable rating sunk to 24 percent, with 56 percent unfavorable.
Republicans were responsible for much of the decline in Gingrich's image. Among them, his favorable rating dropped from 57 percent to 43 percent during the primary — though his positive ratings also fell from 29 to 21 percent among political independents.
Gingrich's image may have recovered somewhat since then, especially among Republicans. A Bloomberg News poll in June found 29 percent of Trump's general-election supporters said Gingrich would be the best running mate on a list of seven Republicans: Sen. Marco Rubio (Fla.) was close behind with 24 percent and Ohio Gov. John Kasich was next at 18 percent (neither of whom appears to be on Trump's short list). A smaller 9 percent said Christie would be the best vice-presidential pick.
One unknown factor for Gingrich is how much he would be hampered by his performance as House speaker in the 1990s, his most prominent moment in politics. His unfavorable ratings hit a high of 59 percent in April of 1998, the year in which Gingrich pressed to impeach President Bill Clinton over the Monica Lewinsky sex scandal. On the flip side, of course, Trump is said to welcome Gingrich's experience battling the Clintons, according to The Post's Robert Costa and Karen Tumulty.
Christie's popularity has been gauged much more in recent months, given his unsuccessful run for the GOP nomination this year. A June CNN-ORC poll found 35 percent of registered voters rate Christie favorably and 45 percent unfavorably. A 57 percent majority of Republicans see Christie positively, while he is in net-negative territory among independents.
That modestly negative image contrasts sharply with Christie's initial entrance to the national political arena, when his response to Hurricane Sandy in 2012 led to broad appeal. A 2013 Pew Research Center poll found 40 percent rating Christie favorably, while 17 percent were unfavorable, including 2-to-1 positive ratings among Democrats. But Christie's bipartisan image faded after the Bridgegate scandal and other political battles.
Washington Post-ABC News polling in 2015 showed deeply negative views of Christie, with about twice as many Americans viewing him unfavorably (51 percent in March and 48 percent in May) than favorably (26 percent and 22 percent, respectively). By January, Christie had improved somewhat, but he was still 12 points underwater (47 percent unfavorable, versus 35 percent favorable). Back home in New Jersey, he remains vastly unpopular.
How do Clinton's potential running mates compare to Gingrich and Christie? In large part, we don't know, as national polls have not tested favorable ratings of four of the top five prospects ranked by Fix boss Chris Cillizza: Housing and Urban Development Secretary Julian Castro and Sens. Sherrod Brown (Ohio), Timothy M. Kaine (Va.) and Amy Klobuchar (Minn.). Other than the fifth, Sen. Elizabeth Warren (Mass.), it's likely that many Americans have not heard a great deal about these Democrats at this point, bringing neither a strongly positive or negative reputation to Clinton's ticket.
A recent Monmouth poll showed Warren, Kaine and Castro as Clinton's VP turned on about as many people as it turned off, but about half of Americans didn't have an opinion about any of them. Back home, Kaine had a narrowly positive image in a recent Roanoke College poll of Virginia, while Quinnipiac polling finds Brown's job approval rating is more clearly in positive territory in Ohio.
While perhaps a less likely pick, Warren received mixed national reviews in the aforementioned CNN poll. About as many had a favorable opinion of her as unfavorable (28 percent vs. 27 percent), while 44 percent had no opinion of the senator.
It's likely both Christie and Gingrich's images will shift if they join Trump's ticket, receiving a massive boost in attention along with a boost in support from Republicans and decrease among Democrats. But while both prospects may assuage concerns about Trump's lack of political experience, they are unable to lend the candidacy broad personal popularity.
Emily Guskin contributed to this report.