The second proposal would allow voters to only recall a legislative official if he or she has bee accused of malfeasance.
"There has to be some standard, where there has to at least be a firm accusation with some type of foundation of credibility," state Rep. David Craig (R) told the Washington Post in support of the bills.
After the initial votes Thursday, the first measure regarding statewide officials would need to pass additional votes and be placed on the ballot as a referendum in 2014, according to the Post. The second bill, which applies to legislative officials, would not need a popular vote, according to Reuters.
Wisconsin Gov. Scott Walker (R) survived a tough recall election in June 2012 after he stripped most collective bargaining rights from Wisconsin public employees, provoking backlash from Democrats.