For Liberals everywhere, Mike Baird’s handsome win in Saturday’s New South Wales election was a huge relief.

His Coalition government suffered an almost nine per cent swing against it but such was the landslide last time it merely restored a more business-as-usual look to the lower house in the parliament.

Foreign Minister Julie Bishop was very upfront on what the vote meant for brand Liberal in Canberra. She said it “removed an obstacle” on the road to recovery. She didn’t say for Tony Abbott, but she didn’t have to.

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The federal Coalition is in dire political straits because of the Prime Minister’s less-than-impressive performance since taking the treasury benches.

Her senior Liberal colleague Scott Morrison hailed the result as important for the national economy and the budget. He made absolutely no concessions that it meant anything for the Prime Minister, because he says Mr Baird was merely emulating Mr Abbott.

That curious claim is based on the fact that the Prime Minister took to the election an agenda which he has delivered on. You know: boats, carbon and mining taxes all gone. Mr Baird, he says, is now promising to implement his agenda the people have similarly embraced.

Reasons to smile: Mike Baird (left) and Tony Abbott before the NSW election. Photo: AAP

Mr Morrison’s view conveniently ignores the gross breach of trust that was the first Abbott government budget. Where basically every promise on what they would not do was broken.

A former interstate Liberal campaign director doubts that the party’s win in NSW can restore the credibility Mr Abbott has lost. For that he points to the standing of the federal government over the long term in the opinion polls.

The difference between Mr Baird and Mr Abbott could not be starker.

Mr Baird is the most popular political leader in Australia. Mr Abbott is the least popular. Mr Baird’s government was never headed by Labor in the polls, while Mr Abbott’s has trailed since December 2013.

Polling analyst Andrew Catsaras says the Coalition has suffered a 6.2 per cent primary vote swing and a 6.5 per cent two-party-preferred swing since the 2013 election. The trend in the polls has the federal government on a trajectory to defeat.

Of course, things can change. The party room in Canberra might take heart from the example of a change to a more user-friendly leader and jettison the toxic Mr Abbott for the vastly more popular Malcolm Turnbull, or even Ms Bishop.

The degree of difficulty is much higher. Mr Abbott, unlike premiers Barry O’Farrell or Ted Baillieu in Victoria, would not go quietly.

A bloody transition followed by a brooding or vengeful dumped Prime Minister and Treasurer could do more harm than good. Everybody seems to agree Treasurer Joe Hockey’s fate is tied to the incumbent leader. That, more than Saturday’s result, will certainly buy more time for both men.

Mr Abbott spelt out his recovery strategy earlier in the weekend. He said he has a “relentless focus since February on the things that really matter to people”.

The May budget will be the next big test.

Paul Bongiorno AM is a veteran of the Canberra Press Gallery, with 40 years’ experience covering Australian politics. He is Contributing Editor for Network Ten, appears on Radio National Breakfast and writes a weekly column on national affairs for The New Daily. He tweets at @PaulBongiorno