Last year, the court found that Canadians born abroad received a lower class of citizenship than those born in Canada, and it gave the government until June 19 to correct the problem.
Miller introduced a bill on May 23 that would allow Canadians who were born abroad to pass their citizenship down to their children, and asked the court for a deadline extension the following day.
NDP immigration critic Jenny Kwan made two attempts to push the bill through the legislative process more quickly by asking for the unanimous consent of MPs, but Conservatives voted no both times.
"We have no time to waste and we have to get the law passed," Kwan said at a press conference Tuesday.
In 2009, former Conservative prime minister Stephen Harper's government changed the law so that Canadian parents who were abroad could not pass down their citizenship, unless their child was born in Canada.
Those who've not had access to citizenship rights as a result of the amendments are known as "Lost Canadians."
Kwan said the House of Commons immigration committee already studied the issue of Lost Canadians when it considered a Senate public bill brought forward by Conservative Sen. Yonah Martin last year.
"We spent over 30 hours at committee debating Bill S-245," said Kwan.
That bill was heavily amended by Kwan and Liberal members of the committee to grant citizenship to a broader group of people, but the Conservatives felt the changes were too drastic and have not brought it back to the House for third reading.
