The state Senate Rules Committee is scheduled to consider the measure on Monday.
The Indiana House approved the proposal last month after nixing hotly contested language that also would ban same-sex civil unions.
The amendment won broad bipartisan support in 2011 and must pass the Legislature again this session to go to voters in a November referendum. The House’s move to leave out the amendment’s so-called “second sentence” that would ban same-sex civil unions could jeopardize that and delay the vote for another two years.
Gov. Mike Pence says he supports the original proposal and has refused to comment further as lawmakers hash out the details.
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