A 'now hiring' sign is displayed in a business's window in Manhattan on Jan. 9, 2026, in New York City. Spencer Platt | Getty Images Federal labor market data issued Tuesday suggests the frozen U.S. job market may be starting to thaw — but the economic fallout from the Iran war threatens to stall that momentum , according to labor economists. "Is the hiring recession finally over? There are encouraging signs," Heather Long, chief economist at Navy Federal Credit Union, wrote in an e-mail. "The big concern is the war in Iran could halt that much needed progress in the labor market," she wrote. Job market 'may be stabilizing' The labor market has been in a so-called " low hire, low fire " mode for more than a year, characterized by a low rate of hiring, layoffs and voluntary quits among workers.…