"There's a case for paid parental leave, there's a case for more money for melanoma drugs, there's a case for more intervention for people who are homeless, and we have just got to weigh all those up."
It brings to an end a four-year fight by Ms Moroney to extend paid leave.
The Labour MP said yesterday she was "frustrated and disappointed" by the veto. The Government had "ignored democracy" and "put politics ahead of people".
"It is backed by the majority of New Zealanders and the majority of our Parliament," the Labour MP said. "It is backed by all the research and evidence. The only people who are opposed to this are the National Party."
A similar bill also in Ms Moroney's name was voted down in early 2015, but the balance of power shifted when National lost the Northland seat to New Zealand First leader Winston Peters.
Ms Moroney's second bill was supported by the Greens, New Zealand First, the Maori Party and United Future, giving it the 61 votes required to pass into law.
It will return to Parliament for a third reading on June 29, but it will be a futile exercise.
United Future leader Peter Dunne, who wants an eventual increase to 52 weeks, said there was a "delicious irony" in the Government's veto.
"Yesterday Government was saying that putting children at the centre of policy was priority," he said. "Today they ban a bill on paid parental leave."
Mr English has used the financial veto seven times in the last eight years, but mostly on non-contentious changes to larger bills.
Former Labour Finance Minister Michael Cullen used the veto 15 times in the previous nine years, again on amendments.
Treasury estimated the cost of Ms Moroney's bill at $278 million over four years - "a significant extra, unbudgeted cost," Mr English said.
"That's on top of the $251 million a year (net of tax) taxpayers are expected to spend by 2020 under the existing paid parental leave framework."
The Government has extended paid parental leave from 14 to 18 weeks and made casual and seasonal workers eligible for compensation.
Mr English would not rule out further increases yesterday: "I am sure it will remain part of the political discussion".
Story so far
April 2012: Labour bill to extend paid parental leave from 14 weeks to 26 weeks pulled from ballot.
July 2014: The bill gets support in initial stages, and Govt signals it will veto it. It does not pass before the 2014 general election.
May 2014: Govt confirms plan to lift paid leave to 18 weeks.
September 2014: National wins election, gains an extra seat.
February 2015: The bill returns to Parliament and fails, having lost its majority support.
March 2015: NZ First leader Winston Peters wins Northland seat, changes balance of power in Parliament.
July 2015: Sue Moroney has a new bill extending leave to 26 weeks pulled from ballot, which passes its first and second stages.
June 16, 2016: Govt vetoes Moroney's bill.