Every other party leader in Parliament has now called for the Government to respond more generously to the plight of Syrians fleeing their homeland -- including government support partners Act leader David Seymour, United Future leader Peter Dunne and the Maori Party.
However, the Labour and Green Party bills are unlikely to be successful -- trying to get bills introduced by leave of Parliament can be blocked if just one MP objects and the Government will almost certainly block it.
Mr Little denied it was a stunt.
"Parliament needs to show leadership where the Prime Minister has not. By the time Mr Key does his review more lives will be lost."
He said the Government had managed to pass a law to allow bars to open during Rugby World Cup games - a far less serious matter.
Last year New Zealand set aside 100 places for Syrian refugees but only 83 were filled because the remaining 17 refugees had either declined because they did not want to settle in New Zealand, or failed medical requirements.
Mr Little said the UNHCR has sent out a call to countries including New Zealand to take more refugees so clearly believed there was a need.
"We have Syrian communities here so it is possible to relocate refugees here to New Zealand and have them in or close to communities of their people. I think we have to make that opportunity available."
Mr Key initially ruled out any urgent measures such as an emergency intake, saying he would wait for a review of the quota next year. Since then he has signalled the government will look at some extra intake of refugees or a further allocation of places within the quota for Syrians. That could be discussed on Monday at Cabinet.
Mr Little said if Mr Key did move on the issue on Monday he would be delighted.
"If he does that I would welcome that and welcome the opportunity to work cooperatively with the Government to make sure we do have an intake above our existing quota. If we get the chance to do that, fantastic."
Labour and the Green parties intend to support each other's bills and other parties are expected to consider them at caucus on Tuesday.