The US treasury department has warned the US risks default if Congress does not authorise more borrowing by August.
Mr Biden said it was now up to President Obama and leaders of the Republicans and Democrats in Congress to decide on the way forward.
The Republicans are resisting Democrat proposals for tax rises in any deal.
They say that such tax increases - amounting to as much as $400bn (£249bn) on corporations and the wealthy, according to the Washington Post - will stifle economic recovery.
The Democrats oppose Republican proposals for steep cuts to health and retirement programmes.
The two sides need to reach an agreement that will enable Congress to raise the $14.29tr (£8.7tr) debt ceiling before 2 August, or the US risks defaulting on its debt.
This could send the US back into recession and throw global markets into turmoil. (read more)