Christie criticized the idea that the president could cozy up to Vladimir Putin, noting that all recent presidents have failed to engage Putin by not being tough enough. He then hit Trump for having said that Putin was "brilliant and a great leader." As the night has worn on, Christie continues to be really the only candidate who is bothering to attack the guy who is 40 or more points ahead of every other candidate in national GOP primary polls.

— Analysis by Geoffrey Skelley of 538

Ilia Calderón is asking about sending U.S. troops to Mexico. In a late August/early September survey by Morning Consult, 41 percent of Republicans said they thought that sending U.S. troops to fight cartels in Mexico would be “very effective” at limiting the supply of illegal drugs in the United States. Other strategies had more support among Republicans, such as sending more resources to the U.S.-Mexico border (54 percent), empowering U.S. law enforcement to combat opioids (45 percent), and punishing drug violators in the United States (43 percent).
—Analysis by 538

Haley going after Ramaswamy was a recurring theme in the first debate. They were the standout candidates in our polling last time and there was a lot of speculation about Ramaswamy moving up in the polls — perhaps even surpassing DeSantis. But since August, Ramaswamy has actually lost support, to the point where Haley passed him in our polling average today. It makes sense that they're trading blows again; this seems to be a successful strategy for Haley, and Ramaswamy can't help but take the bait.
-Analysis by G. Elliott Morris of 538

The candidates are discussing support for Ukraine. About half (49 percent) of Republicans and Republican-leaning independents say that vital U.S. interests are not really at stake in the war in Ukraine, according to an August Echelon Insights survey. Thirty-seven percent disagree, saying that if Russia wins, vital U.S. interests and values are threatened. Fourteen percent are unsure.
—Analysis by 538

This is False.

Pence has used this 90 percent drop statistic many times, but has never explained where it comes from.

When the COVID-19 pandemic started, immigration drastically dropped worldwide as governments enacted policies limiting people’s movement. In the U.S., Trump instituted Title 42, a public health policy that authorized the Border Patrol to immediately return most immigrants back to Mexico. The increased use of this policy decreased the use of other programs, including "Remain in Mexico."

U.S. Customs and Border Protection during the pandemic also adopted a new way of reporting migrant encounters. Before the pandemic, it only reported enforcement actions under immigration law; its data during the pandemic includes actions taken under both immigration law and the public health policy. Therefore, 2020 data isn’t entirely comparable to pre-pandemic numbers.

Accounting for challenges in data comparisons, our review found an increase of 300 percent in illegal immigration from Trump’s first full month in office, February 2017, to his last full month, December 2020.

One way to get close to Pence’s alleged 90 percent decrease in illegal immigration is by comparing data from May 2019, the month during the administration that had the highest apprehensions, to April 2020, the month with the lowest enforcement actions in calendar year 2020.

But that’s a severely cherry-picked time period.
-Analysis by Aaron Sharockman, PolitiFact