At Pizzetteria Brunetti, a restaurant in Manhattan's West Village, owner Jason Brunetti said he would soon end overtime and cut employee hours. Delivery workers will have additional duties, such as chopping wood for the pizza oven.
"They're not just going to stand there and wait for deliveries, that's for sure," said Mr. Brunetti, who is planning these changes because he expects his payroll to rise $700 a week after New York's new minimum wages take effect.
On Thursday, the state's minimum wage increases to $9 an hour from $8.75. The hourly minimum wages for tipped workers--which were $4.90 for service employees at resort hotels, $5 for food-service workers and $5.65 for other service workers--all go to $7.50.
For fast-food workers, the hourly minimum wage increases to $10.50 in New York City and $9.75 in the rest of the state as part of a gradual phase-in of a $15 minimum hourly wage at restaurants with at least 30 locations nationwide.
The rising wages mark the latest chapter in a long-simmering political battle over worker pay in New York and across the country.
When the next legislative session begins in Albany in January, Gov. Andrew Cuomo, a Democrat, is expected to face an uphill battle as he advances a proposal to increase the state minimum wage to $15 an hour.
The governor is expected to release specifics on his minimum-wage proposal when he delivers his State of the State address on Jan. 13. He has indicated that the $15 wage would be gradually phased in and include a tax cut for businesses affected by the rising wages.
This year, Mr. Cuomo sidestepped the Legislature and got the $15 minimum wage for fast-food workers by instructing his acting labor commissioner to impanel a special wage board to consider an increase for the industry. The board subsequently recommended the increase, the acting labor commissioner approved it and it became law.
But to raise the minimum wage for all workers in the state, Mr. Cuomo will need the Legislature.
Reflecting a national debate, the legislative battle in Albany generally splits along party lines: Democrats support raising the minimum wage, and Republicans are resistant to it.
The GOP-led state Senate has previously opposed proposed increases in the minimum wage, but Majority Leader John Flanagan, a Long Island Republican, recently said he is "open to discussions" on the issue.
This year, the fight over the minimum wage will take place when every seat in the Legislature is up for election.
Assemblywoman Linda Rosenthal, a Manhattan Democrat who supports a wage increase, said it was fair game for Democrats campaigning against Republicans to use their opposition to a higher wage against them.
"People always start off by saying 'this can't pass, that can't pass,' if something's hard to do," she said. "But a lot of things happen in Albany that surprises everyone."
Some Republicans said they are vehemently opposed.
"It would be a disaster, particularly for upstate New York," said Ed Cox, chairman of the state Republican Party. "This is all driven by Cuomo's personal ambitions and politics, not by policy."
Supporters of a wage increase say it will help the economy by expanding the middle-class, and that cities that have begun phasing in a $15 wage haven't suffered for it.
In New York, wages for about 100,000 employees in fast-food chain restaurants statewide will increase Thursday, said James Parrott, deputy director and chief economist at the Fiscal Policy Institute, a liberal-leaning research organization.
Those in the restaurant industry, particularly in smaller-scale operations, said they are particularly hard hit. "It's really creating quite a crisis in the fine-dining industry," said Robert Bookman, counsel to the New York City Hospitality Alliance, an industry group.
The increase in the tipped minimum wage will further exacerbate the difference in pay between servers and cooks and dishwashers, he said.
The New York State Restaurant Association, a trade group, sent a letter Tuesday to Mr. Cuomo and other government officials seeking a five-year freeze in the minimum wage for tipped workers. "We simply cannot weather a continuous barrage of labor cost increases," said the letter, which was signed by more than 100 restaurant owners.
For members of the New York State Hospitality & Tourism Association, a hotel trade group, the increasing tipped wage "is forcing business owners to look at overall operations and staffing needs like never before," said Mark Dorr, the association's vice president.
Henry's at the Farm, a restaurant at Buttermilk Falls Inn in the Hudson Valley, plans to raise menu prices, said owner Robert Pollock.
"We'll probably have to raise our costs of food and have smaller portions of proteins on the menu," he said. "That's what most people are doing."
Fernando Paredes, who said he currently earns $7 an hour, plus tips, making deliveries on a bicycle for Dunhill Cafe & Caterers in Midtown, welcomed the expected 50-cent-an-hour raise.
"It's good news," said Mr. Paredes, 39, who lives in Brooklyn and said he plans to use the extra money for subway fare and other things that have risen in price. "Any penny counts, right?"
Write to Corinne Ramey at Corinne.Ramey@wsj.com and Mike Vilensky at email@example.com