After more than an hour of talks, there was no deal and both sides blamed each other.
House of Representatives speaker John Boehner said Mr Obama refused to negotiate, while House Democratic leader Nancy Pelosi and Senate majority leader Harry Reid accused Republicans of trying to hold the President hostage over his healthcare reforms.
Mr Reid said Mr Obama told Republicans "he will not stand" for their tactics. The White House said Mr Obama remains hopeful "common sense will prevail".
However, there was little to encourage hope for a quick solution to the shutdown and hundreds of thousands of federal employees remain at home without pay.
Leaders of the Republican- controlled House of Representatives and the Democratic-led Senate offered token concessions that were quickly dismissed by the other side. Republicans have tried to tie continued government funding to measures that would undercut Mr Obama's signature healthcare law, but the President and his Democrats say that is a non-starter.
Mr Boehner said: "The President reiterated one more time that he will not negotiate."