Such a move would remove exemptions from the ban currently enjoyed by bars and taverns.
The current budget passed by the House cuts $3 million from the health department's Tobacco Prevention and Cessation program.
Johnson County officials voted to repeal the ban before it went into effect Jan. 1 after concerns were raised from local businesses.
Despite a city council vote of 4-2 for the ban, some residents say they are not pleased.
The Columbus ordinance is stricter than the state smoking ban that provides exemptions for bars, taverns and private clubs.
After tabling the measure last month, the council will likely vote on the smoking ban Tuesday.
Johnson County's non-smoking ordinance is stricter than the statewide smoking ban, as well as the bans in Frankiln and Greenwood.
The Columbus City Council tabled a vote to enforce a smoking ban that would include bars, restaurants and clubs.
Lawrence Mayor Dean Jessup says the ban is meant to protect the health of Lawrence residents.
Some employers are already charging different rates to smokers. Labor leaders say they worry about a trend where many health habits are legislated against.