Midway through this month’s special legislative session, Gov. John Bel Edwards seems likely to raise no more than $450 million of the $600 million of new tax revenue that he says is needed, and even reaching that amount presents a major challenge.

The Louisiana House has raised only about $225 million so far, but its leadership has agreed to have the Ways and Means Committee hear a measure on Wednesday that would produce another $115 million by limiting a federal tax deduction taken on state returns mostly by upper-income taxpayers.

Beyond that, it’s not clear how the governor could raise much more, given the resistance among Republicans in the House.

“If we get to $450 million, I’d be awfully happy,” Senate President John Alario, R-Westwego, told reporters Tuesday. “That’s a difficult target to reach.”

“The public should be prepared that TOPS will not be fully funded, that K-12 schools will not be fully funded and that the safety net hospitals will not be fully funded,” state Sen. JP Morrell, D-New Orleans, who chairs the Senate tax-writing committee, said in a separate interview. “At the end of the day, there’s not enough money.”

In legislative terms, it’s actually not the end of the day. The current 18-day second special session ends on June 23, in time for state officials to determine how much money is available for the new fiscal year that begins on July 1.

But the House has rejected Edwards’ measures that would produce at least $600 million for next year.

“If the Legislature fails to raise revenue, then the cuts will come July 1,” Ben Nevers, the governor’s chief of staff, told reporters on Friday.

Edwards’ best hope for having enough money to limit those cuts is House Bill 38 by freshman Rep. Malinda White, D-Bogalusa, which appears likely to pass the Ways and Means Committee on Wednesday with the addition of several amendments.

White’s bill would eliminate about half the deduction that taxpayers get on their state income taxes by itemizing such items as their state and local tax payments, gambling losses, charitable contributions and mortgage interest payments. The Ways and Means Committee last week narrowly defeated a similar bill.

Breathing life into White’s bill are amendments restoring the income tax break in 2018, ensuring that taxpayers who itemize will continue to be able to take the deduction for charitable contributions and mortgage payments, and rebating the tax payments to taxpayers if the state collects more money than expected by 2018. State Rep. Jim Morris, R-Oil City and a staunch tax opponent, said in an interview Tuesday that he and state Rep. Neil Abramson, D-New Orleans, are prepared to vote for White’s bill if it includes their changes.

Morris and Abramson, who are the vice chairman and chairman of the Ways and Means Committee, respectively, both voted against last week’s bill that limited the itemized deductions but also made other changes to tax law. Because that bill was defeated 10-9, their support likely would ensure passage of White’s bill.

Edwards met with both men on Monday to discuss White’s bill and is scheduled to meet with them again on Wednesday before the committee takes it up.

“It is critically important,” Edwards said in an interview at the Governor’s Mansion following a bill signing. “We are far too short of the needed revenue to fund critical priorities. This is a major component in that.”

Alario said he is looking at ways to amend tax bills already approved by the House — that are now before the Senate — to raise more dollars. Even if he succeeds in doing that, however, the tax-averse House would have to approve the changes.

“They get a rash evidently whenever a tax comes before them,” Alario said of the House. “I hope they find a salve for it.”

Alario’s salve could be a new proposal that would force companies to choose which of two lucrative tax breaks to keep, if they qualify for both.

The two tax breaks they would have to choose between are the industrial tax exemption on local property taxes and the inventory tax credit, where some businesses get reimbursed by the state for a portion of the local property taxes that they pay.

State Sen. Rick Ward, R-Port Allen, is the sponsor of the measure, Senate Bill 10. He said it could raise up to $170 million next year and mostly would hit large manufacturing companies.

“We’re putting you in a position where you have to pick,” Morrell said of the companies.

Morrell added that the measure is projected to raise money for the state — and not local governments — because “I have not found one instance where a company is getting more from the inventory tax credit than from the industrial tax exemption.”

The Senate Revenue and Fiscal Affairs Committee, which Morrell chairs, will hear SB10 on Wednesday and is likely to send it to the full Senate.

The measure’s chances of passing both the Senate and the House don’t seem promising, however, because it would raise taxes on big companies that have a small army of lobbyists to kill it.

Making sure to spend time with Ward on Tuesday were two of those lobbyists, Chris John, president of the Louisiana Mid-Continent Oil and Gas Association, and Gregory Bowser, the director of governmental affairs for the Louisiana Chemical Association.

Meanwhile, Morrell reversed position and decided to have his committee approve a measure aimed at restoring sales tax breaks that benefit some two dozen nonprofits. The Legislature inadvertently eliminated those sales tax breaks in the chaotic finish of the first special session in March.

Morrell said the House leadership’s decision to take up White’s bill in the Ways and Means Committee and the House’s passage of a small tax bill on Monday were enough for him to lift his committee’s hold on the measure, Senate Bill 3.

It would restore the sales tax exemption on sales and donations to food banks, garage sales and food sales for groups like the Boys Scouts. It would not affect the sale of Girls Scout Cookies — as The Advocate reported Monday — because they did not lose their sales tax exemption, Kim Robinson, revenue secretary, said in an interview.

Mark Ballard, of The Advocate’s Capitol news bureau, contributed to this report. Follow Tyler Bridges on Twitter, @TegBridges. For more coverage of government and politics, follow our Politics Blog at http://blogs.the advocate.com/politicsblog.