House Speaker Michael E. Busch, an Anne Arundel County Democrat, has been supportive of allowing same-sex couples to marry, though not outspokenly so.
Republicans gained six seats in the November election.
Dwyer and Mitchell predicted that a vote on the House floor would be close.
"I think there will be supporters of the bill in the House who will have second thoughts," said Dwyer, who called himself the face of the opposition.
Already one of the legislation's original 59 co-sponsors has asked that his name be removed.
Del. Melvin L. Stukes said he thought the House bill, titled the Religious Freedom and Civil Marriage Protection Act, would have given same-sex couples the right to join in civil unions. The Baltimore Democrat learned in recent weeks that it would grant full marriage benefits, which he said he has never supported.
"I don't want to deny anybody their human or civil rights," he said. "But to me, marriage is a moral issue. I could pull out the Scriptures on it. I'm very sorry that I got on the bill."
Several Democrats from conservative-leaning areas, including Dels. Norman H. Conway of the Eastern Shore and Michael H. Weir Jr. of Baltimore County, have said they will vote against the bill. And some black lawmakers with strong ties to their churches, including Dels. Cheryl D. Glenn of Baltimore and Emmett C. Burns Jr. of Baltimore County, are against it.
House Republicans voted weeks ago to oppose any legislation that would change the state's definition of marriage. But it is not clear that all Republicans would vote against the measure. Some Republicans said Thursday that they prefer to remain silent for now.
In the Senate, former Minority Leader Allan H. Kittleman, whose district includes Howard and Carroll counties, gave up his leadership post after fellow Republicans expressed anger at his support for civil unions. He ultimately scrapped his civil unions bill and voted Thursday to support same-sex marriage. He was the only Senate Republican to cast a "yes" vote.
Del. Veronica L. Turner said she is torn about how to vote and needs to learn more about the legislation. The Prince George's County Democrat said she will try to excuse herself from the Health and Government Operations Committee on which she serves to listen to the debate Friday in the Judiciary Committee.
"I need to hear both sides for myself," she said. "I want to make sure I'm very educated about this before making my decision."
Baltimore Sun researcher Paul McCardell contributed to this article.
Senate votes 25-21 to approve gay marriage
House to begin hearing bill on Friday
Gov. Martin O'Malley says he would sign it