As of Monday, Labor candidate Michael Holland was on track to take the seat of Bega, the first time his party has won the seat, and Labor looked to retain Strathfield.

The Nationals retained Monaro and the Liberals retained Willoughby despite an 18 per cent swing to an independent candidate.

"The bottom line is when the two former members of the government benches, [John] Sidoti and [Gareth] Ward, vote for the government and everyone votes against them, the government will now rely on the Speaker's vote to pass legislation," Dr McGirr said.

"They will be relying on the Speaker [of the House's] casting vote; now that is very tight. You don't want anyone missing the vote.

"It also means you are relying on the goodwill of Sidoti and Ward, so I think it makes the situation significantly more tense."

Dr McGirr said he would continue to support budget supply for the Coalition in the interests of "good, stable government".

"That's important for the state and for the electorate," he said.

Wagga-based Nationals MLC Wes Fang said he did not think Saturday's byelection results would make it harder for the Coalition government to pass legislation.

"I think that, for the most part, the crossbench are broadly supportive of what the government is doing in the legislative sense," he said.

"Even before the byelections came up, we were particularly good with consulting and engaging with opposition and crossbenchers and I think there is a lot of goodwill towards the government.

"They have recognised that we have done a strong job in handling the pandemic and actually governing for the past two-and-a-half years, so I don't see it is going to be a problem."

Mr Fang attributed the Bega loss to "localised" issues and said the swing against Labor in Strathfield was also a significant result.

Dr McGirr met with NSW Premier Dominic Perrottet along with the two other independent NSW MPs on Wednesday.

"We emphasised the importance of full and timely briefings so that we can fully assess upcoming legislation," Dr McGirr said.

Dr McGirr said he would not have another chance to meet Mr Perrottet before Parliament resumed this week.

Mr Perrottet described the byelection results as "disappointing" on Sunday.

"I think ultimately when you are in a pandemic you are going to make decisions that from time to time will be unpopular. Our job as a government is to take our state through and we are doing that," he said.

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