Marriage equality will be the first test of Bill Shorten and Malcolm Turnbull's commitment to find common ground in the new Parliament – but don't hold your breath on a joint approach.

The common ground is that both leaders support it, but both are committed to different paths to achieve it and are neither is likely to budge.

Eight days after the vote, Shorten has conceded what the Australian Electoral Commission is yet to declare: that Turnbull will have the numbers in the lower house to form a government, either as a minority government or with a majority of one or two seats.

Not a moment too soon, the rancorous tone of the marathon campaign has given way to a measure of grace and humility from both leaders and a recognition that the voters have had a gutful of division and are yearning for something better.

Whether they get it is something else altogether, given Shorten's prediction that the Coalition will be forced back the polls within the year and the other pressures on Turnbull.

These include dealing with an emboldened National Party, a resentful conservative flank and a much more challenging Senate crossbench.

Shorten has promised to be constructive and there is potential for consensus in areas including some aspects of budget repair, with superannuation the most likely. Given the task facing the Coalition to protect the AAA credit rating, negative gearing and capital gains tax concessions could also be in the frame for discussion.

For Turnbull, it makes sense to explore what is possible with Labor and the Greens on big-ticket items before seeking individual agreements with the likes of Pauline Hanson on the Senate crossbench.

Marriage equality will have to be tackled soon after the new government is sworn in and Turnbull will be anxious to win support for legislation for the national plebiscite that Shorten and the Greens have opposed on the grounds that it is unnecessary and potentially divisive and destructive.

Shorten and the Greens's Richard Di Natale will argue that the question should be put to the Parliament – a course that would be vigorously opposed by Coalition conservatives led by Tony Abbott.

One possible compromise would be for Labor and the Greens to agree to support a plebiscite if a vote by MPs did not resolve the issue, though this is unlikely to fly.

Either way, we won't have to wait long before we know whether the promise to work together will extend beyond a commitment to introduce electronic voting.