ALBANY – Democrats are resisting efforts by Senate Republicans to permit employers to offer a “training wage” to workers younger than 20 as a way to protect some companies from having to give a minimum-wage increase to all employees.

The issue was among those being discussed in closed-door meetings Sunday at the Capitol as Gov. Andrew M. Cuomo and legislative leaders sought to resolve their remaining sticking points before the State Legislature returns here today.

Sources close to the talks say issues involving the minimum wage, tax breaks for middle-class families and small businesses, and Cuomo’s proposal to relax marijuana-possession laws are among the final major issues the sides are wrestling with as they try to pass a budget for the fiscal year beginning April 1.

Senate Republicans have warmed to the idea of a minimum-wage increase, after more than a year of opposition, to $7.25 per hour, but only if it is linked to tax breaks, including possibly raising the dollar amount for deduction of dependents on state income tax filings or to boost the child tax credit.

Also on the table is extending the expiration of a higher income tax bracket, which starts at $1 million for single filer taxpayers, that brings the state about $2 billion a year in revenues. That higher tax bracket, approved in December 2011, is due to expire in 2014, when Cuomo and the Legislature are up for re-election.

Democrats say the Senate GOP’s proposal to exempt employers from boosting the minimum wage increase – to some as-yet unsettled level – for young people is unfair and would hurt many of the people who need the higher salaries. But Senate co-leader Dean G. Skelos, a Long Island Republican, said in an interview at the Capitol on Sunday evening that many employers would be forced to lay off teenagers if a minimum-wage increase goes through without protections for some businesses and not-for-profits.

“It’s really a youth wage. A lot of businesses, whether it’s agriculture or camps, those types of things, they have many young people that work there, [and] if we do a full minimum wage of some sort, it could negatively impact them,” Skelos said.

“So for young people who have high unemployment, especially in the minority communities, a youth wage would protect them if there’s an increase in the minimum wage.”

The Senate proposal, Skelos said, would apply to workers younger than 20.

The sides are still discussing a figure for a minimum wage hike, whether to phase it in over a few years and whether it would be indexed for annual increases based on the inflation rate.

Secrecy reigned at the Capitol on Sunday, and some officials appeared little interested in keeping reporters aware that talks were even taking place. The governor, for instance, issued a public schedule saying he was to be in the “New York City area” on Sunday. Cuomo aides said the governor did not arrive in Albany until Sunday afternoon.

Senate co-leader Jeffrey D. Klein, D-Bronx, said that there is still no deal on the minimum-wage hike but that there is “an understanding that we have to do the minimum wage.” Talks have centered on an increase of $1 or more in the current hourly wage level.

Assembly Speaker Sheldon Silver, D-Manhattan, said that talks are continuing but that “a lot of major issues”’ remain unresolved.

Asked about the major sticking point, Silver said, “Time. … We have to conclude, so it’s crunch time.”

Lawmakers are trying to adopt a budget by Thursday or Friday. To do so with Cuomo giving the usual three-day aging process for legislation – a process often ignored during the budget deliberations – bills would have to be printed by Tuesday night for a Friday final passage before lawmakers leave Albany for the religious holidays and a spring break.

“I think we’re closing down a lot of the major issues,” Skelos said while heading to a meeting with Cuomo. “Right now, for the Senate Republicans, it’s critically important that we get business-friendly tax cuts, especially for small businesses, job creation, family tax cuts, many of which we’ve proposed this year and in the past. And then I think we can close this budget down.”

The halls of the Capitol on Sunday afternoon saw a steady stream of legislative and administration fiscal staff members. Gone from most was the usual Albany suit, replaced by casual wear, as the prolonged talks have made sleep the most sought-after commodity for negotiators in the final days.