Gov. Gretchen Whitmer of Michigan is betting that the photo was worth it. When she went to the White House this month for her ill-fated meeting with President Trump — the one where she hid her face from a New York Times photographer — she had been trying to secure funding for an expansion of Selfridge Air National Guard Base near Detroit. So when Mr. Trump traveled to Michigan on Tuesday to announce on his 100th day in office that he was doing precisely what Ms. Whitmer had asked for, she had cause for a victory lap — despite the possible cost to her political prospects. She greeted him upon his arrival, creating another photo of them together, and then briefly stood beside him to make remarks thanking him for expanding the base. “The fact that we got it done — all the grief is worth it,” Ms. Whitmer said in an interview after the event on Tuesday. “The people of Michigan elected me twice because they know whether it’s threats or pundits ridiculing me for going to the White House, I’m always going to stand up for the people of Michigan.” In Michigan, Ms. Whitmer and her allies view the expansion at Selfridge as a big enough victory to be worth whatever personal humiliation she endured. The Defense Department will station about 20 F-15EX fighter jets at the base beginning in 2028, according to a document it circulated to Michigan’s senators.