Topeka ? Gov. Sam Brownback said Monday that Kansas legislators are taking a “workman-like” approach to sifting through proposals for raising taxes to close a state budget shortfall, praising them after their annual session went into overtime with no plan having passed either chamber.

The Republican governor opened a Statehouse news conference by congratulating the GOP-dominated Legislature for “really working well.” He said drafting a tax plan is difficult because in involves discussions among many lawmakers about many options.

Brownback and lawmakers must close a projected shortfall of $406 million in the state budget for the fiscal year beginning July 1. The gap arose after lawmakers aggressively cut personal income taxes in 2012 and 2013 at Brownback’s urging in an effort to stimulate the economy, and one policy exempted the profits of 281,000 business owners and 53,000 farmers from taxation.

The governor views the tax break for farmers and business owners, viewing it as an economic stimulus, but even some GOP lawmakers want to backtrack. A new proposal for narrowing the tax break emerged Monday in the House.

Legislators also are considering increasing the state’s 6.15 percent sales tax, an idea Brownback now favors.

“There’s a great workman-like attitude,” Brownback said. “These things take a lot of time because you’ve got a lot of people involved, a lot of moving parts. That’s great. That’s what it ought to be.”

Legislators met Monday for the 92nd day of their annual session, two more than the 90 days legislative leaders traditionally schedule, at a total cost of $43,000 per day. Only five legislative sessions have lasted 100 days or more, according to legislative researchers, with the record of 107 days set in 2002.

Republican Rep. Don Hineman of Dighton was skeptical of Brownback’s sunny assessment, saying, “We’ll see if folks are still talking that way when the calendar says June 1.”

The House last week voted down a plan last week that would have increased the sales tax to 6.85 percent. Several Republicans said afterward that the vote suggested the House did not want such a big increase in the sales tax.

The chamber’s Taxation Committee was supposed to convene Monday to work on a new revenue-raising plan, but it postponed several sessions during the day and ultimately met only briefly. It introduced the new proposal to narrow the tax break for business owners and farmers and scheduled a hearing for Tuesday.

The new proposal would exempt only the first $150,000 of profits for business owners and farmers for this year and the first $100,000 for 2016 each year afterward. The committee’s chairman, Republican Rep. Marvin Kleeb, of Overland Park, said the measure could raise between $45 million and $55 million during the next fiscal year.

“I’m not saying we even want to do it, but this is an idea that’s floating around out there,” Kleeb said.

Democrats argue that increasing the sales tax would hurt poor and working-class families more than wealthier ones, though recent proposals would drop the rate on food. Rep. Tom Sawyer, of Wichita, the Taxation Committee’s ranking Democrat, said the new proposal represents at least a little progress.

“I think it’s a good sign that they’re willing to talk about closing that loophole for businesses,” Sawyer said.

But Influential business groups are lobbying to preserve the tax exemption, including the Kansas Chamber of Commerce and the National Federation of Independent Business. They contend that a change would hurt growth and send a bad signal to companies that might want to expand or relocate.