"We asked Michael Cohen about this extensively", said Schiff.
"I think the country is worth it".
"It's our job to protect the rule of law", he said.
Trump and the White House also argue that Cohen's track record of lying means he can't be believed - that he'll say anything to save his image and try to get a lighter punishment for other crimes he's admitted to.
Current Justice Department orthodoxy is that a sitting president can not be indicted, but Schiff believes this needs to be reevaluated.
After months of expressing certainty over a Trump impeachment-and even an indictment that would land the ex-president in prison-Schiff's softening of his stance could be the latest indicator that Democrats are expecting the findings of Special Counselor Robert Mueller to be underwhelming and anticlimactic.
The chairman echoed the position of House Speaker Nancy Pelosi from her interview on Monday and said that without buy-in from congressional Republicans - who control the Senate - embarking upon the process today would be "doomed for failure". "The only thing worse than putting the country through the trauma of an impeachment is putting the country through the trauma of a failed impeachment".
Democrats have been careful not to close the door entirely, however.
Schiff, D-Calif., told NBC News' Meet the Press that he believes a face-to-face interview with Trump would be the most effective method to get information regarding any potential collusion with Russian Federation by Trump or his campaign during the election or possible obstruction of justice into the probe.
'If the Justice Department the position that you can not indict a sitting president, when the president is no longer sitting then I think it has to consider whether it should hold a former president to a different standard than it holds everyone else, ' Schiff said - making sure to state that the decision should be in the hands of career prosecutors based on the evidence they gather.
Schiff said his committee is particularly interested in whether Russian Federation was laundering money for the Trump Organization, leading to Trump being compromised.
"Well, if there's insufficient evidence in the Mueller report and we're not able to produce sufficient evidence in our own investigation, that ends the inquiry", Schiff explained. Trump's comment came as CNN reported that the Justice Department may announce as early as next week that Mueller has given Barr his report on the probe.
'We have already seen deeply concerning evidence of the president's lack of fitness for office.