In this file photo, Rep. Steve Carter, R-Baton Rouge, crosses the House floor. Carter said he is optimistic House Bill 632, which would raise the state gas tax 17 cents per gallon, and raise $510 million per year for roads, bridges and other forms of transportation, will pass a House Ways and Committee vote on Tuesday.

Backers of a state gasoline tax increase need something of a political miracle, and the first test is set for Tuesday in a Louisiana House committee that has been killing tax bills.

With just over four weeks left in the 2017 regular legislative session, supporters of the drive for new dollars for roads and bridges hope the longshot effort is about to get going.

The initial votes are scheduled for Tuesday in the House Ways and Means Committee, which has rejected a wide range of tax plans, including those offered by Gov. John Bel Edwards, to address state budget problems.

Backers of new state aid for roads and bridges insist they are not discouraged.

"I am very optimistic," said state Rep. Steve Carter, R-Baton Rouge.

"But you can't wait any longer," Carter added. "We are right at the point where if we don't do what we have to do, then we are going to be too late."

Carter is the sponsor of House Bill 632, which would raise the state gas tax 17 cents per gallon, and raise $510 million per year for roads, bridges and other forms of transportation.

It would also link the state's gasoline tax to the Consumer Price Index, which could gradually raise it another 13 cents per gallon.

Also on the agenda is House Bill 561, which would increase the state sales tax by half a cent, raise $428 million for transportation and have to win both legislative and voter approval to take effect.

Rep. Sam Jones, D-Franklin, sponsor of the sales tax bill, said Friday he is unsure how to proceed, and has been conferring with Carter.

"Maybe at the end of the day we will coalesce ideas and come up with something," he said.

Carter's plan is to get the bill out of Ways and Means, then see if backers can cobble together the always daunting two-thirds majority – 70 votes – needed for approval in the full House.

And all this has to happen in a session dominated by efforts to tackle state budget problems, and regular bickering between House leaders and Edwards.

If the bills fail in committee that may end debate on the issue for the session.

House Transportation Committee Chairman Kenny Havard, R-St. Francisville, who had his own tax measure battered and killed by Ways and Means earlier this month, said he doubts any gas tax increase will emerge from the House.

"That is just the reality of the situation," Havard said.

Senate Transportation Committee Chairman Page Cortez, R-Lafayette, said Friday he too doubts there is enough support.

"From my perspective, it doesn't look like they can get 70 votes on anything in the House," said Cortez, who served for four years in the lower chamber.

"I don't mean to knock them," he added. "They are pulling in different directions."

Motorists pay 38.4 cents per gallon for gasoline, including 20 cents in state charges.

A task force named by Edwards recommended a $700 million annual hike in transportation spending.

However, Carter's 17 cent increase is seen as more politically feasible, and the one that most backers of an increase are rallying around.

Shawn Wilson, co-chair of the task force and the governors' transportation lieutenant, said getting a gas tax hike through the Legislature was always a heavy lift because of the mood of voters and lawmakers. "I think we needed a Hail Mary on transportation in general," Wilson said. 

But Wilson said that, unlike other tax debates in the State Capitol, most everyone agrees that Louisiana needs transportation improvements.

"It is something that can still be achieved, it is something that remains a bipartisan issue," he said of the legislation. "We are still committed to trying to make it happen."

Edwards has said he would back most any bill that is in keeping with his task force recommendations, and historically that would have been enough to give the issue a huge boost.

But the governor has not endorsed Carter's or any other gas tax hike, largely because even allies say doing so would damage efforts for passage.

Cortez said that, rather than the Legislature alone approving a gas tax, a constitutional amendment to let voters decide the issue, like Jones favors, might have a better chance of getting 70 votes in the House.

The cry for congestion relief appears to resonate most in south Louisiana metro areas, including the chronically congested Baton Rouge area as well as Lafayette and New Orleans.

Officials of the Louisiana branch of Americans for Prosperity, a conservative advocacy group, urged members of the House Ways and Means Committee to reject any increases and said lawmakers will be "graded" on their votes.

"Committee members know raising the gas tax will hurt Louisiana families who are already struggling to get by in our state's sluggish economy," AFP-LA State Director John Kay said in a statement after the committee hearings were announced Friday.

The drive to enact a gas tax increase is backed by a 34-member coalition called BUILD IT – Businesses United for Improving Louisiana's Development by Investing in Transportation.

Members include the Baton Rouge Area Chamber, Greater New Orleans Regional Economic Alliance, or GNO; Jefferson Chamber of Commerce; New Orleans Chamber; Louisiana Chemical Association and One Acadiana.

Scott Kirkpatrick, executive director of CRISIS, a transportation advocacy group that is part of the coalition, said Friday he is confident Carter's bill can win approval in the House panel.

"There is certainly plenty of time left in the process," Kirkpatrick said. 

"I think we have some good momentum, and I think members understand this deserves a full discussion on the House floor," he said.

The session ends June 8.

Follow Will Sentell on Twitter, @WillSentell.