Prominent right-wing media commentators have sought for weeks to cast aspersions on the House impeachment inquiry into President Trump, echoing the president’s repeated cries of “witch hunt!” and framing the investigation as motivated by political bias.

Now some of those commentators have opened a new front: questioning the patriotism of Lt. Col. Alexander S. Vindman, the White House national security official and decorated Iraq war veteran who was testifying on Tuesday that he had heard Mr. Trump ask Ukraine to investigate his Democratic political rival.

One pundit on Fox News went as far as to suggest that Colonel Vindman had engaged in “espionage” against the United States, prompting an unusual rebuke from a Republican member of Congress.

Colonel Vindman, who received a Purple Heart after he was wounded in Iraq, is a Ukrainian-American immigrant who was 3 years old when his family fled to the United States. On her Fox News program on Monday, the conservative host Laura Ingraham sought to turn his ethnic background against him, noting that Ukrainian officials had recently sought the colonel’s advice about interacting with Mr. Trump’s personal lawyer, Rudolph W. Giuliani.