DFL Gov. Tim Walz and GOP lawmakers in St. Paul failed to meet a self-imposed deadline Monday to broadly agree on how much to spend on schools, health care and other major areas of the state's budget.

The two sides called financial negotiations "positive" and "respectful" Monday afternoon, but said their approaches to setting a budget are fundamentally opposed.

The depth of their differences was clear Monday night. After meetings throughout the day, Walz, House Democrats and Senate Republicans made some concessions, but held firm on their positions on a health care provider tax and transportation funding.

Lawmakers set the Monday deadline months ago for reaching spending targets. They are aiming for an organized end to the session and to avoid returning to the Capitol to finish negotiations after the Legislature adjourns May 20. The Democratic governor, DFL-led House and Senate Republican majority have been working through a $2 billion difference in their spending plans.

E-12 education is one of the key areas where the parties differ, Walz said Monday. There is a roughly $700 million chasm between what Democrats and Republicans envision spending on schools over the next two years.

Walz questioned the Senate's spending plan, which aims to avoid raising taxes, and called it "an arbitrary number that they set ideologically."

Meanwhile Senate Majority Leader Paul Gazelka, R-Nisswa, condemned the DFL approach to budgeting. He said the governor and House DFL leaders built their budgets by adding in spending priorities, and then raised taxes as necessary to pay for them.

Gazelka, Walz and House Speaker Melissa Hortman, DFL-Brooklyn Park, are trying to determine the top-line number for the state's next two-year budget, and within that, what should be spent on education or health and human services. Legislators have already started meeting in joint conference committees, and need to know those numbers so they have goals to work toward as they merge House and Senate budget bills.

Walz's plan for a 20-cent-per-gallon gas tax increase remained another key area of division between the parties.

"The gas tax is not going to happen," Gazelka said Monday. He said that is one of a few areas where Senate Republicans have drawn a "strong red line."

Gazelka said he is open to using some state-backed borrowing to fund additional road and bridge projects, but declined to comment in detail about the possibility of an infrastructure bonding bill this session.

"No scenario that they put out … keeps pace with what Minnesota needs to do to keep a high-quality state transportation system," Walz said of the GOP's opposition to the gas tax. "So that is an ongoing discussion."