BATON ROUGE (AP) — As deep budget cuts threaten state services and jobs, Gov. Bobby Jindal told lawmakers on the opening day of the annual regular session Monday that the money troubles also provide a chance to change the way Louisiana does business.

‘‘It is our job to give our people a new Louisiana so our children and our grandchildren can pursue their dreams without leaving home. I know we’ve got enormous challenges, but these are enormous opportunities,’’ Jindal told a joint session of the House and Senate.

Louisiana’s financial difficulties have overshadowed other debates, as lawmakers, state agencies and public colleges brace for more budget cuts — on top of three rounds of reductions levied over the past year and a half.

‘‘The state’s no different than a family. You have to do things differently when there’s less money,’’ said Sen. Danny Martiny, R-Kenner. ‘‘But I’m sure the people that are going to get cut aren’t going to look at it as an opportunity.’’

A deficit of up to $400 million is projected for the remaining three months of the current fiscal year, and lawmakers will have to rebalance this year’s budget before they can devise a final plan for next year.

Sen. Karen Carter Peterson of New Orleans said this session would be the most difficult she’s seen in her decade in the Legislature.

Jindal proposed a mix of one-time funding and cuts to balance next year’s $24.2 billion budget. Disagreements have already emerged between the House and Senate about how much should be trimmed and how much state trust funds should be tapped to fill gaps in the 2010-11 fiscal year that begins July 1.

Rep. Joe Harrison, R-Napoleonville, said the budget problems are only projected to worsen. ‘‘We have to get rid of the frills and fund the necessities,’’ he said. ‘‘We need to cut more now.’’

In his speech, the governor said lawmakers need to unlock some of the state funds that are dedicated to specific programs, ease the ability to tap into state trust funds in difficult budget years and tie dollars to performance standards.

Jindal contrasted his approach to the state budget problems with that of Washington officials, saying Louisiana won’t raise taxes or deficit-spend to cope with the wide-ranging shortfalls. Neither is allowable anyway: Tax increases can’t be considered in the regular session this year, and the state is constitutionally required to maintain a balanced budget each year.

But Sen. Robert Adley, R-Benton, and other lawmakers said if Jindal wants to undo some of the provisions that link fees to specific programs and use those dollars more widely throughout the budget, that would equate to a tax hike.

Divisions quickly emerged Monday over one of Jindal’s proposals, a bill that would let public colleges substantially raise tuition without a vote of lawmakers if the schools meet certain performance benchmarks.

Some lawmakers said it was inappropriate to raise costs on students in the tight economy, while others said the funding would help universities improve their graduation rates and give students a better education.

LSU student leaders and a group of about three dozen students worked the Capitol hallways, asking lawmakers to support the tuition increase bill and avoid more cuts to higher education.

‘‘I’m willing to pay for my education and the value of my education,’’ said Martina Scheuermann, LSU student government vice president.

However, another group from the university — including campus instructors and faculty and calling itself Save LSU — circulated a statement saying tuition hikes would hurt students and the school and wouldn’t generate enough money to replace dollars already cut from LSU.

Another one of this session’s most heated disputes is expected to center on a bill by Sen. A.G. Crowe, R-Slidell, attempting to nullify the federal health care overhaul, arguing the congressional legislation is unconstitutional.

Tea party groups in the state have made Crowe’s bill one of their top priorities for passage in the session, while the Legislature’s black caucus is vowing to fight it. Dozens of people from the Baton Rouge Tea Party and other tea party organizations rallied on the Capitol steps Monday to support Crowe’s bill.

Lawmakers are also debating looser gun restrictions, a red light camera ban, tougher laws for drunk drivers and sex offenders, changes to state ethics laws and other issues.

The legislative session runs until June 21.

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On the Net:

Louisiana Legislature: www.legis.state.la.us