JUNEAU — The floor of the Alaska Senate broke into an impromptu debate over oil taxes Monday.

Sen. Cathy Giessel sparked the discussion in a special order, which is when members speak on issues of their own choosing. Hers was entitled “What Could It Look Like?”

Giessel, R-Anchorage, and chair of the Senate Resources Committee, spoke of the need for a healthy oil industry for Alaska’s economy and what alternatives Alaska had for comparable tax revenues. They included having tens of thousands of cruise ships visit Alaska, every Alaskan of drinking age down 138 shots a day and every Alaskan of age smoke 10 packs of cigarette a day. She said those aren’t things the state would want to do.

Giessel said there is new activity on the North Slope under the rewrite of Alaska’s oil production tax, which the Legislature passed last year. The state is better protected at lower oil prices under the new law and the new system would yield more revenues if prices continued to fall than under the former tax structure, she said.

She is much happier to see the activity on Point Thomson and additional rigs on the North Slope than the alternative, Giessel said.

Sens. Hollis French and Bill Wielechowski offered rebuttals.

French, the Senate minority leader, in a speech he entitled “Another Idea,” said the state also could “undo that bad tax idea and put a fair oil tax back on the books.”

Alaska under the new system will never capture windfall profits when oil taxes spike as the state did under the old system, he said.

A referendum on the tax law is scheduled for the August primary ballot. French said Alaskans can go to the polls and vote to fix the tax, allowing lawmakers to work on putting a fair tax on the books.

Wielechowski, D-Anchorage, in his remarks, entitled “Where’s the Production?” said Gov. Sean Parnell “promised us, told us” there would be more production — including 1 million barrels of oil — if the oil-tax change was passed. But he said forecasts call for continued production declines. He called the bill “a complete and utter failure.”

Parnell, when he began seeking an overhaul in the oil-tax structure several years ago, set a goal of 1 million barrels of oil a day through the trans-Alaska pipeline system in a decade. The Department of Natural Resources in 2012 said that during that period, the target could include sources like development of smaller pools of conventional oil, production from shale and heavy oil plays and production from the Arctic National Wildlife Refuge, which state officials have been pushing to have opened to drilling. The refuge remains off limits to drilling, however.

During the tax debate last year, oil company officials said they believed the tax cut would lead to more production, but it wasn’t clear just how much more and when the increased production would happen.

People on both sides of the tax debate have at different times sought to use the tax structure as at least part of the reason for the long-term trend of declining production. It happened during the push to change taxes in 2011 and 2012 — which ultimately culminated in the passage of the new system last year — and is being used by opponents of the new tax structure, who say the state’s lower revenues are just the start of problems if the tax stands. The current fiscal year was divided between the old tax structure and the new one.

In an interview, Wielechowski said the tax structure actually has “very little” impact on production and that there are other steps the state can take to encourage new investment. He said Democrats are considering rolling out a new proposal this session that would offer Alaskans a view of what a new tax structure might look like, if the referendum to repeal the current one is successful.

Parnell spokeswoman Sharon Leighow said by email Friday that Parnell’s goal included production from the Arctic National Wildlife Refuge, portions of the National Petroleum Reserve-Alaska and offshore. Shell recently announced it was halting operations off Alaska’s Arctic shores this year and possibly withdrawing for good, in part after an adverse court decision.

“However,” Leighow said, “we remain very optimistic for Alaska’s oil future, especially with the billions of dollars in new investment we’ve seen already.”