Arriving in Luxembourg for a meeting of the Foreign Affairs Council, Hunt said: "I can't tell you that I'm very confident or not confident. We are going into these talks sincerely and we have to see what the outcome is."
EU leaders are divided about what to do if the British politicians fail to strike a deal among themselves.
May has lost three votes on her Brexit deal, with ardent Brexiteers and Eurosceptic Conservatives joining forces to defeat it.
The passage of the bill in parliament on Monday came as talks between May and Jeremy Corbyn, the opposition Labour leader, failed to break the current Brexit deadlock.
It also came hours before May's trip to Berlin and Paris on Tuesday, when the prime minister will hold talks with German Chancellor Angela Merkel and French President Emmanuel Macron for a delay of the Brexit date, which has been pushed back from March 29 to April 12, May's spokesman said Monday.
May also spoke by phone to many other European leaders ahead of Wednesday's EU summit, during which she is expected to seek a second extension to Britain's exit date from the EU.
Britain's impasse over Brexit casts a cloud of uncertainty over the EU leaders' meeting for emergency talks in Brussels on Wednesday.
The leaders from 27 EU member states are frustrated with all the Brexit wrangling. They had agreed that April 12 will be the Brexit date, if by then May still has not got the withdrawal agreement passed by parliament.
Michel Barnier, the EU's chief Brexit negotiator, was in Dublin on Monday for talks with Irish Prime Minister Leo Varadkar.
They discussed developments in London as well as preparations for a possible no-deal scenario.