The Supreme Court was one reason for wavering conservatives to back Trump in November. More Republicans than Democrats said the Supreme Court was a major factor in their vote. Trump has pleased them with this choice.The election was close enough that a lot of things might have swung it. Certainly I spoke to people who said that they were single-issue voters this last time around, and that single issue was the Supreme Court. I suspect many people who had serious concerns about Trump nevertheless saw in Clinton's potential election the end of the Constitution as they understood it. If Scalia had still been alive and on the court as a guardian of that Constitution, would it have been enough to swing enough votes to the other side?
He has also given himself a rare breath of normalcy in a turbulent first two weeks on the job. Amid continuing chaos over the refugee ban and increased resistance from Democrats to Trump’s Cabinet nominees, picking a well-respected jurist with a solid conservative reputation might be the most traditionally presidential thing Trump has done in office.
By following through on his pledge here, I expect Trump has won himself some ground with any voters who did choose him to protect the Supreme Court. Keeping your word builds credibility, and credibility is the currency. If he keeps doing this, the next time he seeks their vote he might get it on his own account. Of course, he'll have to keep it up.