Republicans in the state Legislature flatly rejected the notion of passing one particular bill that would increase the minimum wage on Tuesday, but left plenty of wiggle room to eventually support a compromise.

“It’s not that I’m totally against an increase in the minimum wage,” said Assemblyman Kenneth D. Blankenbush, the Black River Republican who voted against the Assembly Democratic majority’s version of the hike. “I just feel like a 17 percent increase, plus (automatic increases to) adjust it every year, is something that I couldn’t support.”

The measure passed the Democratic-dominated lower chamber on Tuesday but Republicans said it wouldn’t pass in the Senate, which they control.

But it might not be the end of the road for some sort of minimum wage hike.

Senate Majority Leader Dean Skelos, R-Long Island, narrowly responded at a news conference that: “I’m just telling you, we will not pass the speaker’s bill.”

That leaves a wide berth for compromise, which could change the terms of the current proposal, which is to increase the minimum wage from $7.25 an hour to $8.50 an hour. The minimum wage would rise yearly with the rate of inflation.

State Sen. Patricia A. Ritchie, R-Heuvelton, also left room for compromise while rejecting the bill passed on Tuesday by the Assembly.

“Senator Ritchie does not support the bill passed by the Assembly,” Graham Wise, her chief of staff, said in an email. “She is concerned that this particular legislation will hinder, not help, job creation in her district.”

In a follow-up message about whether she was leaving room to eventually support a minimum wage increase, Mr. Wise said: “She has not seen any proposal that she can support.”

Mr. Blankenbush held a roundtable discussion on the matter in Gouverneur. He said that mostly small businesses showed up, and that nobody supported an increase in the minimum wage. He suggested that the agriculture community, which is subject to the whims of a volatile market, should be exempted from the increase. The Republicans in the Senate and the Democrats in the Assembly could reach some sort of compromise that would get rid of the yearly increases, Mr. Blankenbush said. It might also involve tax breaks for small businesses, a proposal that Senate Republicans put forth earlier this year.

“If a minimum wage bill is to be passed this year, it would have to be a different bill with compromises in that bill,” he said.

Assemblywoman Addie J. Russell, D-Theresa, voted to approve the measure, though she conceded that it didn’t really have a chance in the Senate. Striking a populist tone, Mrs. Russell said increasing the minimum wage could help stimulate the economy by putting more back in the pockets of working families.

“We have gone down the corporate welfare road, and those types of policies just don’t appear to be working,” she said. “We have very large employers who are just sitting on piles of cash and are not hiring.”

She, too, was open to compromise, saying that the final bill may not include an annual increase in the minimum wage.

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