The Republican-led House approved the amendment last month. The measure must pass both the House and Senate again in 2013 or 2013 to go to before voters on the 2014 ballot.
If it wins full passage this year, the measure would still have to be approved by the next legislature and then by Indiana voters in order for the state Constitution to be amended.
The committee will vote on the measure in a week. If it clears the legislature this year, it must again be approved by the next General Assembly and by voters in 2014 in order for the Constitution to be amended.
A Senate committee will take up the issue later this week. The House has already approved the proposal, and the Senate is expected to pass it as well.
The protesters say the amendment would write discrimination into the state constitution.
A gay marriage amendment passed the General Assembly in 2005, but it has to clear two legislatures and a public referendum in order to be put into the Constitution.