Quebec's political leaders are looking for a way to defuse a conflict over the provincial budget that could trigger the second provincial election in a matter of months.

Premier Jean Charest is looking to compromise on the provincial budget but will stop short of doing away with the massive tax cut that threatens his minority government.

"I can assure that a dialogue has begun," Finance Minister Monique Jerome-Forget told a Montreal Chamber of Commerce luncheon on Monday. "I will do everything humanly possible to resolve and bring about an end to this impasse."

The Liberals are expected to offer the Parti Quebecois a deal on Tuesday that will maintain the nearly $1 billion proposed tax cut while increasing provisions for home care and students with special needs.

Charest made appearances on French-language supper-hour newscasts to try and put pressure on the two opposition parties.

"The real question is where is the will of (PQ leadership hopeful) Pauline Marois and Mr. (ADQ Leader Mario) Dumont," Charest told television network TVA. "Because if there is an election on June 1, it will be them who pressed the button."

The PQ and the Action Democratique du Quebec have threatened to vote against the Liberal budget on Friday unless a major overhaul is undertaken.

The PQ had hoped for more health care and education spending in the budget, while the ADQ wanted to see some paying down of the provincial deficit before major tax cuts.

Jerome-Forget said on Sunday the tax cuts were non-negotiable.

While Premier Jean Charest has tried to paint the cuts as making his government the defender of the middle class, the policy doesn't seem to be that popular.

According to a poll released Monday by Leger Marketing, 56 per cent of Quebecers don't want an election, but 70 per cent opposed the tax cuts.

They'd rather see new spending or a pay-down of the provincial debt.

Most ominously for Charest, his Liberals would finish third if an election were held right now. They would capture only 28 per cent of the vote, their lowest total ever and the same support the PQ got in the March 26 election.

In that contest, the Liberals won 48 seats in the 125-seat legislature, compared with 41 for the ADQ and 36 for the PQ.

In the poll, the ADQ would capture 33 per cent of the vote, and the PQ would form the opposition with 30 per cent.

"He must reach an agreement today because if we have an election today, he will lost," pollster Jean-Marc Leger said of Charest.

The poll was conducted between May 23 and 26. Leger interviewed 1,001 people, meaning the margin of error is plus or minus 3.1 percentage points.

While the Liberals have incentive to find a way out of this situation, the government insists the tax cut is still non-negotiable.

"It seems we have to fight for that, but we will do that -- we will fight to decrease your taxes," Philippe Couillard, Quebec's health minister, said Monday at a news conference.

Despite the talk of talks on Tuesday, Couillard would only say they had not been confirmed.

With reports from CTV's Jed Kahane and John Grant, and files from The Canadian Press