The Louisiana House passed an uneventful day during a short session Sunday afternoon. The Senate didn’t meet.

The real work begins Monday.

The Senate will debate and pass its version of the $24 billion state budget, which is House Bill 1.

The House, meanwhile, on Monday or Tuesday will take up 10 tax bills passed by the Senate last week and is expected to reject most if not all of them. Approval of the tax bills is needed to fund the next year’s budget.

Both chambers are moving toward a final showdown on Thursday when they have until 6 p.m. — when the legislative session ends — to approve a budget that doesn’t contain deep cuts to public health care and public colleges and universities — and doesn’t run afoul of Gov. Bobby Jindal’s demand that it not contain a net tax increase.

Whether the Legislature can raise enough money without inviting a budget veto by Jindal remains an open question, lawmakers said Sunday.

“We’re still working hard on it,” said state Rep. Chris Broadwater, R-Hammond, who is one of the lawmakers working behind the scenes to craft a solution.

State Sen. President John Alario, R-Westwego, has acknowledged that the budget will inevitably include so many short-term fixes that the governor and state legislators who take office in January will inherit a major budget deficit — as much as $1 billion. One of the uncertainties before the Legislature now is whether the Senate raised enough money Friday and Saturday to fully fund about $750 million in extra spending in its version of the budget to fund the higher education institutions and public health care.

House staff was still trying to determine on Sunday how much the Senate raised after amending the 10 tax bills. An early estimate was $176 million more than the $615 million raised by the House, meaning the Senate is now proposing to raise a total of $791 million more next year.

About $120 million of the $176 million in extra revenue approved by the Senate would come from increasing the cigarette tax by 72 cents per pack — not 32 cents as the House did — and raising taxes on other tobacco products.

The Senate’s increases on cigarettes and tobacco would raise $188 million compared to $68 million with a 32-cent cigarette tax alone.

The two chambers will have to settle on a final plan through a conference committee that will contain three members from each chamber.

“I don’t know what in the world we’re going to do,” said state Rep. Harold Ritchie, D-Bogalusa, the sponsor of the cigarette tax increase. “I have had a lot of members tell me they can’t vote for the bill (at a 72-cent increase).”

If the House rejects the 72-cent increase in favor of 32 cents — and also rejects the increase on other tobacco products — legislators will have to come up with another $120 million or cut that much in funding for LSU and the other public colleges and universities and the public hospital system.

Besides the cigarette tax, the House and Senate disagree on one other major issue: whether to approve the so-called SAVE fund. The Senate wants it, while the House remains skeptical about it.

The SAVE fund would create a fee of perhaps $1,500 apiece on college and university students and an offsetting tax credit for $1,500. Students wouldn’t actually have to pay anything, and the higher education institutions wouldn’t collect any more money.

Instead, supporters of the SAVE fund say its purpose is to create $350 million or so in paper tax credits that the governor could use to offset $350 million in revenue-raising measures to maintain tax neutrality.

State Rep. John Bel Edwards, D-Amite, in an interview Sunday, called it a “fictitious fee. It’s still an ugly duckling.”

No governor has vetoed the state budget since the state constitution went into effect in 1974. If Jindal does so this year, state Rep. Cameron Henry, R-Metairie, has prepared a resolution saying the House will override the governor with a two-thirds vote. He has more than 85 signatures in the 105-member House for the resolution, Henry said in an interview.

He said he expects to seek approval of the resolution on Monday, along with passage of a supplementary budget to fund state government services during July and August. The House and Senate cannot meet to try to override the governor with a two-thirds vote in each chamber until July 21. Since next year’s budget takes effect on July 1, the supplemental budget would aim to finance state services until the House and Senate finally resolve the budget crisis.

Follow Tyler Bridges on Twitter, @TegBridges. For more coverage of the State Capitol, follow Louisiana Politics at http://blogs.theadvocate.com/politicsblog.