JACKSON (AP) — Lawmakers who travel High Street to reach the Mississippi Capitol get a daily reminder about an issue that hasn’t gone away despite the efforts of Gov. Haley Barbour.

A billboard with the image of smiling children on one side and a pack of Marlboro cigarettes on the other asks the question: ‘‘Whose side are you on: Big Tobacco or Mississippi’s children?’’

The stark, black-and-white backdrop of the billboard is an apt depiction of a tax swap proposal that gained momentum in 2006 before fizzling under Barbour’s veto. The bill would have raised the 18-cents-a-pack excise tax on cigarettes and cut the state’s 7 percent grocery tax.

An attempt to pass a similar bill last year was killed by one of Barbour’s allies who chaired a Senate committee.

Many lawmakers say the reason they’ll continue to push for passage is simple: Mississippi has one of the highest grocery tax rates in the nation, and one of the lowest excise taxes on cigarettes.

‘‘Primarily, I think we’re going to be looking at some kind of way to increase it and earmark it for Medicaid or the state’s trauma system,’’ said House Ways and Means Chairman Percy Watson, D-Hattiesburg.

‘‘We have a statutory constitutional duty to do what we feel is in the best interest of the state,’’ said Watson, referring to the need to generate revenue at time when some state agencies are facing multimillion dollar deficits.

There are at least five tobacco tax bills referred to Watson’s committee. Sixteen states allocate some cigarette tax revenues to health programs, according to the Washington, D.C.-based Campaign for Tobacco Free Kids. Tobacco taxes have been raised in 12 states over the last year, the campaign said.

Barbour, a Republican, just started his second term as governor. He is a former Washington lobbyist whose clients included some tobacco companies. He says repeatedly that he is opposed to raising taxes.

The governor has proposed other ways to plug budget holes, including streamlining government agencies and imposing what he calls an assessment on hospitals; critics say the assessment is simply a tax.

Lt. Gov. Phil Bryant, a fellow Republican, presides over the Senate where a roadblock is waiting for any tobacco tax bills.

The Coalition of Communities for a Clean Bill of Health, the group that sponsored the billboard, has conducted research that shows a $1 tax on a pack of cigarettes would generate $150 million annually. The group gave lawmakers copies of the survey last week.

The coalition has gained an ally in the Mississippi Hospital Association, which is more vocal in its support of a cigarette tax this year. MHA sees a tobacco tax a a better option than taxing the state’s public and private hospitals.

Barbour wants to levy a 1.5 percent tax on the gross revenue of hospitals to shore up the budget of Medicaid, a health care program that receives both state and federal dollars.

The program, which serves 568,000 of the state’s poor, elderly and disabled, faces a $92 million budget shortfall the fiscal year that ends June 30. Medicaid is asking for at least $268 million in extra funding for the year that starts July 1.

‘‘We do not think that hospital patients should be taxed to pay for a state-federal program,’’ said MHA president and CEO Sam Cameron. ‘‘We believe the state should put a $1 tax on tobacco because a lot of the health-related issues come from tobacco.’’

The Legislature would have to approve Barbour’s hospital tax proposal.

In 2006, Barbour imposed a tax on hospitals to generate $45 million to cover a shortfall in Medicaid. The association sued, questioning whether Barbour had a constitutional right to levy the tax. The governor withdrew the tax, saying federal funding for Hurricane Katrina recovery would cover the Medicaid hole.

Cameron said the association wouldn’t file another lawsuit over the tax. He said MHA was working with lawmakers to ‘‘explore other funding options’’ for Medicaid.

Bryant said it’s ‘‘very unlikely’’ a cigarette tax would make it out of the Senate until a commission appointed by Barbour completes a study of the state’s tax structure in August.

‘‘What our proposal is now is to balance our budget. To use the revenue we have now to fully fund our Medicaid costs and to be reasonable in our expenditures,’’ Bryant said.

Bryant supports Barbour’s plan to exempt several agencies from the oversight of the state Personnel Board, which provides job protection to state employees.

Barbour has said the Department of Corrections and the state Agriculture Department reduced agency spending after the oversight was remove since it allows directors to hire and fire at will.

‘‘We’re talking about ’right-sizing’ state government,’’ Bryant said, borrowing a phrase from Barbour.

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The bills are House Bills 20, 22, 73, 209, and 371.