Woo Senator Lindsey Graham

All throughout the campaign, Mr. Bush had made a point of texting Senator Lindsey Graham of South Carolina weekly, just to check in. On the morning Mr. Graham dropped out of the race for president, Mr. Bush was ready with the hard sell.

Mr. Bush immediately sent him a quick message, and the two men spoke on the phone later that day, when Mr. Bush made his pitch — that he was best prepared to be commander-in-chief and most qualified on Mr. Graham’s key issue, national security.

Mr. Graham has publicly said he has no plans to endorse anyone right now. Many believe that privately, however, he is strongly leaning toward Mr. Bush, but that he does not want to support him unless he thinks Mr. Bush can actually win the nomination.

Meanwhile, Mr. Bush has already picked up the endorsement of over 20 Graham supporters.