Washington (CNN) As his eldest son faced the prospect of resigning as Delaware's attorney general amid health concerns, Vice President Joe Biden received an offer that floored him: financial support from his boss, President Barack Obama.

In the never been told before story, Biden recalled how concerned Obama had been.

Describing in an interview with CNN chief political analyst Gloria Borger one of his weekly lunches with Obama, Biden said he told the President he was worried about caring for Beau's family without his son's salary.

"I said, 'But I worked it out.'" Biden recalled telling Obama. "I said, 'But -- Jill and I will sell the house and be in good shape.'"

Obama, Biden remembered, pushed back vehemently on the thought of Biden and his wife selling their home in Wilmington, Delaware.

Read More