Gov. Neil Abercrombie, encouraged by a stronger economy, will frame his priorities for the second half of his four-year term on Tuesday when he gives his State of the State address to the Legislature.

The governor’s two-year budget draft is mostly free from the long tail of the recession, an opportunity for him to leave his public-policy stamp on state government.

Abercrombie, who often uses a football analogy to mark time in his administration, is entering the third quarter. Politically, with his job approval rating in the Hawaii Poll under 50 percent since May 2011, he is trailing but slowly clawing back.

"I think he’s got an uphill battle. His public relations, in some people’s eyes, are not the best. Obviously, he’s got to keep himself together with the labor organizations in several different ways," said Dante Carpenter, chairman of the Democratic Party of Hawaii and a longtime ally. "Other than that, because we have a new Legislature this time around, both in the Senate and the House, it’s going to be a challenging period of time."

Abercrombie, who met privately with new state House and Senate leaders on Friday afternoon, will have to quickly forge working relationships with House Speaker Joseph Souki (D, Waihee-Waiehu-Wailuku) and Senate President Donna Mercado Kim (D, Kalihi Valley-Moanalua-Halawa), who took power when the Legislature opened on Wednesday.

The governor will have to navigate contract negotiations with public-sector labor unions that have grown deeply suspicious of a chief executive who once had such a pro-labor reputation when he was a legislator and congressman.

Abercrombie, some of his allies say privately, will also have to avoid undermining his "New Day" agenda by personally stepping into legislative brawls over contentious issues such as the future of the Public Land Development Corp., legalized gambling or even his administration’s support for a soda fee to counter obesity.

"I think it’s going to be an interesting several months," Carpenter said. "This will set the tone one way or the other, if he is on the right track or not, I think."

Abercrombie is expected to use the State of the State speech to amplify the priorities in his budget draft, such as early childhood education through state-funded preschool, investments in information technology to bring state government into the 21st century, replenishing the state’s hurricane relief fund and rainy day fund, and chipping away at the multibillion-dollar unfunded liability in the public worker health care fund.

The governor will also likely stress the importance of keeping Hawaii on track to meet its alternative energy goals. Tesoro’s decision this month to close its refinery — and the potential that Chevron might follow, leaving the state with no refinery — is a reminder of the state’s dependence on imported oil.

Abercrombie may address how money generated from the state’s barrel tax on oil should be distributed. Lawmakers have siphoned money from the barrel tax to help control the budget deficit over the past few years, leaving less available for energy and food security initiatives. He could also discuss how best to preserve tax incentives for solar, which have been restricted by the state Department of Taxation because of concerns about the cost to the state.

"I think the governor, now that he is two years into his term, has an opportunity to get past a lot of the contentiousness and the difficult — especially financial — issues that we had facing us," said Blake Oshiro, the governor’s deputy chief of staff. "So now that things are looking more optimistic, we are hoping that the State of the State will reflect a lot of what we see as the necessary forward progress our state needs to move towards."

At the private meeting with House and Senate leaders on Friday, sources say, there were questions about the potential impact of collective bargaining with public-sector labor unions on the budget. The governor’s budget draft restores the 5 percent sliced from labor over the past two years, but the state has also offered 2 percent annual pay raises in contract talks with public school teachers, and a recent arbitration award for public correctional, institutional and health workers — which included 3.2 percent raises — could set the base for other unions.

Some are worried that labor costs — and the administration’s desire to pay down the unfunded liability in the public worker health care fund — will soak up much of the new revenue and push other state policy priorities into the background.

Abercrombie told reporters last week that the state has to be "very, very careful that collective bargaining doesn’t end up with a war of each against all, with one unit against another, with the young against the old, with the counties against the state."

He added: "My lessons in this, going way back to my introduction to the Legislature, was that you want to try and maximize the opportunity for everybody to be treated fairly. What’s happening right now is a tendency to say ‘Give it to us and not for the others,’ or ‘Others need to sacrifice but we don’t.’"

Advocates of Abercrombie’s state-funded preschool plan hope he uses the State of the State to make a forceful case for early childhood education and answer some of the skeptics who have reservations about cost, quality and implementation.

"There is no doubt that there is research showing the benefits of early education, and that our state is also poised to take it on in this coming legislative session," said Rep. Takashi Ohno (D, Nuuanu-Liliha-Alewa Heights), a former public school teacher and vice chairman of the House Education Committee. "There of course are specifics about the implementation, about how it’s going to be funded. Those are questions that we are looking forward to tackling."

Rep. Beth Fukumoto (R, Mililani-Mililani Mauka-Waipio Acres) said she supports Abercrombie’s potential investment in new information technology and hopes the administration uses it to streamline government bureaucracy for businesses and residents.

She also hopes Abercrombie does not plan to call for tax increases. The governor has said that his financial plan does not rely on new taxes to balance, although his administration is behind a soda fee to generate money to combat obesity.

"I think some of the taxes that he has proposed in the past would really hurt lower-income (residents), and I think we want to avoid that," Fukumoto said.