The married couple and their 5-year-old son were scheduled to arrive in Indianapolis on Wednesday, but the state sent notice to a resettlement organization saying "placement" for that family and another set to enter next month had been "suspended."
The notice set off an 11th-hour search that led the family to Connecticut, where they were welcomed by Gov. Dannel Malloy.
"I told them that people in the United States were generous and good people but sometimes things happen elsewhere that cause people to forget about their generosity," Malloy said at a press conference Wednesday. "I have to say [the family] were absolutely wonderful and charming folks."
The family didn't appear with Malloy at the press conference and their name has not been made public.
During an appearance on MSNBC later, Malloy had harsh words for officials, including House Speaker Paul Ryan, who are pushing to pause refugee resettlement programs.
"There is a certain xenophobic, perhaps racism, involved in what's going on here," Malloy said.
Republicans including Ryan, he added, have chosen "to pick on this specific group because it seems in his mind and other minds to make political sense."
Carleen Miller, the executive director of Exodus, which has been working with the Syrian families, said her agency had resettled 25 Syrian refugees over the past 14 or 15 months.
The State Department, she explained, contracts a collection of nine NGOs to manage refugee arrivals after the federal government completes what are often years of background checks and screenings. Miller's group handles the "on-the-ground work of resettlement."
Though Exodus Refugee Immigration disputes Indiana's legal claim to block the families' arrival, they sought out a more welcoming state government.
"I want us to receive Syrian families, but I was really concerned that this family would be the test case, and they really don't deserve that," Miller told CNN on Thursday.
She also worried the state would deny the refugees needed assistance.
"I was concerned that the family would not get the benefits and services they deserve," Miller said. "We were inundated with calls and media, and I was concerned that the scrutiny would be traumatizing for this new family."
With Indiana not budging, the local group contacted the national office for help.
"They selected a state that had a governor who had not come out against refugees."