Sinn Fein has called for a referendum on a united Ireland following the abortion poll.
Vice president Michelle O'Neill said constitutional issues had gained renewed prominence following Friday's Yes vote on changing the Irish constitution.
She told ITV's Peston On Sunday: "I think in terms of the conversation at home now it's very much about a union referendum, it's very much about the constitutional future.
"The big decision yesterday in Dublin was a constitutional issue, that is now to the fore.
"People who, particularly people from a unionist background who traditionally in the past wouldn't have had this conversation about where they see themselves in the future are now having that conversation and it's a very healthy and live debate."
As part of the 1998 Good Friday Agreement, the British Government accepted the principle of consent, meaning the people of Northern Ireland could decide their own future on the issue.
It recognised the legitimacy of the aspiration for a united Ireland as well as the wish of a majority to remain part of the UK.
The Government has said the time is not right to call a poll on uniting Ireland.
Nationalists have claimed the Brexit result, with its threat of a hard Irish border - which Northern Ireland voted against, had reinvigorated the debate.
Mrs O'Neill said the test had been met for a unity poll.
"I think the fact that if you look at a number of things, the northern state was built on a unionist majority, that unionist majority is now gone."
She said that represented change and the criteria had been met for a unity referendum.