"So many warnings to Turnbull about what the postal vote could unleash", Mr Rudd tweeted from NY.
The High Court challenge was brought by two separate marriage equality groups and argued the government had acted unlawfully to fund the survey using a special reserve of the budget, which sets aside money for matters that are "urgent" and "unforseen".
Nearly half of all Australians eligible to take part in the same-sex marriage postal survey will receive their ballots before the weekend.
Australia are holding a referendum on whether to legalise same-sex marriage, although the results from that are not legally-binding.
According to the interactive, only 43% of voters in the Hinkler electorate support same-sex marriage.
A Columbia Law School project collating conversion therapy research found there was "no credible evidence that sexual orientation can be changed through therapeutic intervention" and that there is "powerful evidence that trying to change a person's sexual orientation can be extremely harmful".
The legislation was introduced because the survey is not covered by the usual safeguards governing elections in Australia.More news: United Nations set for vote on new, albeit softened North Korea sanctions
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"We encourage our fellow Australians to join us in voting yes in the postal survey, which we hope will deliver a positive endorsement of love, respect, freedom and equality before the law". "We pray and fast in a special way for our nation's leaders, we pray that they will uphold God's plan for marriage in our nation", Bishop Kennedy said.
And Mr Shorten reiterated his promise that Labor would ignore a "no" vote under any circumstances, and make same-sex marriage legal if it won government.
Former Prime Minister Tony Abbot is one example.
Some have described the same-sex marriage debate as "marriage equality". You think some people are beneath having rights that you personally enjoy.
"We want this process to be fair and for Australians to get the opportunity to have their say in an appropriate environment", Finance Minister Mathias Cormann said.
The postal survey has drawn controversy over concerns that it will give a platform to hate-filled messages.