The Kansas Statehouse in Topeka

Topeka ? Big questions about taxes and spending will shape the Kansas Legislature’s work after its annual session opens Jan. 9.

But the biggest question might be how much GOP moderates work with conservatives and how often they seek deals with Democrats on tax and budget legislation to protect funding for education and other programs.

Here’s a look at the 2017 session’s biggest questions.

Current budget gap

How will Republican Gov. Sam Brownback propose to eliminate the projected shortfall of more than $345 million in the current budget?

Brownback and his aides haven’t hinted at how he will seek to close the gap, but options are limited.

Legislators can’t raise taxes quickly enough to provide much new revenue before the current fiscal year ends June 30. That suggests spending cuts are likely, though Brownback has ruled out state worker furloughs and across-the-board budget reductions.

Senate President Susan Wagle, of Wichita, and other Republicans have criticized Brownback for not imposing some immediate spending cuts. They haven’t outlined their own proposals.

Brownback and legislators are likely to look for stopgaps to avoid such cuts. For example, State Treasurer Ron Estes said he expects lawmakers to push to pick up about $40 million in gains by liquidating an investment fund the state set up in 2000 to boost its interest earnings.

Longer-term shortfalls

How much appetite do Brownback and his fellow Republicans have for increasing taxes?

The state is facing projected gaps of nearly $1.1 billion in funding for existing programs through June 2019.

Kansas has struggled to balance its budget since GOP legislators slashed personal income taxes in 2012 and 2013 at Brownback’s urging in an effort to stimulate the economy. Even some GOP voters last year came to see the experiment as a bust.

Cuts in income tax rates in 2013 were tied to policies reducing deductions and a sales tax increase to fill budget gaps. Lawmakers boosted sales and cigarette taxes in 2015. A tax increase this year would be the third in five years — something that normally would make legislators wary.

But new House Minority Leader Don Hineman, a Dighton Republican, said: “Let’s do a long-term structural solution to this imbalance that we’ve been dealing with annually for some time now. There’s an appetite for getting that behind us.”

Political context

Elections last year left the Legislature less conservative, with both GOP moderates and Democrats making gains. So who will moderate Republicans work with the most?

Top conservative Republicans appear to have recognized the shift to the center. Both Wagle and incoming House Speaker Ron Ryckman Jr., of Olathe, gave key committee chairmanships to moderates. Hineman’s election as House majority leader was another sign of moderates’ ascendancy.

If Republican lawmakers maintain the early harmony, they could pass legislation without Democratic votes.

If the GOP starts to split, moderates could form coalitions with Democrats on budget and tax issues, as they have in the past. Such a coalition would be more aggressive in seeking to roll back past income tax cuts, pushing for new education spending and resisting spending cuts.

School funding

What will lawmakers do about public school funding, the single biggest item in the state budget?

Republican lawmakers in 2015 junked a per-student formula for distributing more than $4 billion a year in aid to public schools, in favor of predictable “block grants” to the state’s 286 local districts. The block-grant law is set to expire June 30.

While the state’s fiscal woes would seem to preclude additional funds for public schools, lawmakers in both parties are talking about ensuring that their budget fixes raise enough new revenues to allow higher spending on education.

That’s because the Kansas Supreme Court is expected to rule early this year on whether the state is spending enough on its public schools overall to ensure a suitable education for every child. Four districts sued the state in 2010.

Incoming Senate Majority Leader Jim Denning, an Overland Park Republican, predicted that the court would accept a year’s extension of the block-grant law if lawmakers solve the state’s budget problems.

But new House Minority Leader Jim Ward, a Wichita Democrat, said, “That’s like a guy who shows up for his DUI sentencing drunk.”