Speaking on CNN on Thursday, Buttigieg issued his most pointed attack yet on the Massachusetts senator, saying she "was extremely evasive when asked that question, and we've seen that repeatedly."
The sharpened critique comes as the fall campaign kicks into high gear with Iowa's first-in-the-nation caucuses scheduled in February. Warren has assembled a well-organized campaign there and leads Buttigieg in Iowa, where the South Bend, Indiana, mayor's longshot presidential campaign is competing heavily and trying to break through.
"Costs are going to go up for wealthiest Americans, for big corporations," Warren answered when Colbert asked how she would recommend financing the program, and she noted that taxes for the wealthy would go up. "Hardworking middle class families will see their costs go down."
Buttigieg, who noted that Warren answered similarly during last week's debate, said on CNN: "I think it's puzzling."
"Why you wouldn't just say so and then explain why you think that's the better way forward?" Buttigieg asked, noting that Vermont Sen. Bernie Sanders has said his plan to provide "Medicare for All" would raise taxes across the board. "Look, people are used to Washington politicians not giving straight answers to simple questions."
The Warren campaign declined to comment Thursday.
The two candidates, along with 16 of their rivals for the Democratic nomination, are scheduled to descend on Iowa in the coming days, chiefly to appear before thousands of Iowa Democratic activists at a marquee Democratic steak fry fundraiser in Des Moines on Saturday.