BATON ROUGE — Saying they have “unfinished business,” Gov. John Bel Edwards called on lawmakers Tuesday to raise millions of dollars more in taxes aimed at closing budget holes and stopping cuts to health care services and education programs.

Edwards spoke to a joint session of the House and Senate on the first full day of his second special session in five months, laying out his case for $600 million in taxes for the financial year that begins July 1.

“We still have a real mess on our hands, and the longer we put off cleaning up that mess, the more damage we do and the more problems we create for ourselves down the line,” Edwards said.

The Democratic governor is proposing increased income taxes on middle- and upper-income earners, scaled back tax break programs and boosted business taxes.

It’s Edwards’ second special session on taxes since taking office in January. Fatigued lawmakers are questioning whether they’ll support additional tax changes after the litany of tax hikes passed earlier this year, which raised more than $1.2 billion for next year’s budget.

“While we all may be getting weary of what is beginning to look like and feel like a never-ending legislative process, the simple fact of the matter is there is still more important work left to do,” Edwards said. “The people who sent us here expect us to finish the job.”

Some Republicans, particularly in the House, are saying they don’t intend to boost taxes further.

“If it takes money out of someone’s pocket, I’m not for raising taxes on individuals or entities in this session period,” said Rep. Lance Harris, R-Alexandria, chairman of the House GOP delegation.

The 18-day session began Monday night, immediately after the end of the regular legislative session, and must end June 23. It started on a sour note, with House leaders refusing to reach a deal with senators on the multibillion-dollar construction budget for next year, forcing debate over the spending bill to carry into the already contentious special session.

Edwards, however, focused on the state’s $26 billion operating budget in his speech, describing it as “ugly,” with widespread cuts to K-12 public schools, colleges, the TOPS tuition program, safety-net hospitals for the poor and other health services.

Without naming former Gov. Bobby Jindal, Edwards said his predecessor’s budget maneuvers — draining trust funds, patching together spending plans with quick fixes and delaying bill payments — were “tricks and gimmicks” that worsened the state’s financial woes.

“The days of kicking the can down the road are over. The day of reckoning is at hand,” Edwards said.

The full list of items that Edwards included in the parameters for the special session could raise more than $700 million, but Senate leaders have set a $450 million target figure as what was needed to pay for the state’s top priorities.

Half the items included in the special session involve cleaning up the unintended consequences of the last tax session. The final version of a 1-cent state sales tax increase passed in the frenetic closing minutes of that session and swept in school lunches, Girl Scout cookie sales and other items that weren’t meant to be taxed.

Besides the cleanup measures, another item that seems likely to pass is an increase in premium taxes on health care organizations known as HMOs, to draw down additional federal health financing for the state.

Lawmakers passed a similar measure in the first special session, but the formula was rejected by federal health officials. The reworked proposal would generate about $130 million for the budget, according to the Edwards administration.

Harris said he expects the HMO tax will “be an easy one” for passage, but he wants more time to see if the taxes raised in the first special session bring in more money than estimated before agreeing to anything more.

“We’ve done a whole lot of lifting. I think it’s prudent to wait and see,” he said.