The Conservatives have accused the Chancellor of giving an overly pessimistic impression of the public finances as a "smokescreen" to raise taxes. Badenoch claimed Reeves had "lied to the public".
But Downing Street has denied the accusations and Prime Minister Keir Starmer is expected to back Reeves' budget decisions in a speech on Monday, saying the chancellor's decisions will help tackle cost of living pressures and lower inflation.
Opening the interview, Kuenssberg asked Reeves whether she could be trusted and the chancellor responded: "Yes."
Kuenssberg then outlined what the chancellor said in a speech on 4 November, when Reeves indicated there was less cash than previously forecast due to a productivity downgrade, and she was likely going to need to raise taxes as a result.
Reeves explained that, despite what critics were saying, "I didn't have an extra £4bn to play with" but instead that the OBR figures had been downgraded from £9.9bn headroom in spring to £4.2bn in the autumn.
Headroom is the term for money leftover after the government meets its expected budget costs under its own fiscal rules, providing a financial buffer for unexpected costs.
"I clearly could not deliver a budget with just £4.2bn of headroom," she said, as that would have been "the lowest surplus any chancellor ever delivered", and she would "rightly" have been facing criticism for the headroom being too small.
She said: "I was clear that I wanted to build up that resilience and that is why I took those decisions to get that headroom up to £21.7bn."