Albany could be opening its doors this week to state lawmakers and taxing millionaires could be up for discussion.

State officials are attempting to close a $350 million budget gap for the current fiscal year and one projected to be 10 times that in 2012-2013.

Sources say Gov. Andrew Cuomo is considering revamping the tax code so the wealthy pay a little more and the middle class pay a little less.

The New York Times reports that even with the increase, what the wealthy would be paying would be less than the so-called "millionaires' tax" that's set to expire on December 31.

The millionaire's tax that's expiring isn't just for millionaires. It's actually a surcharge on people who make $200,000 or more.

What the governor is reportedly considering would increase what some higher tax brackets are paying, but less than what they're paying now under the surcharge.

"It does appear that this issue is on the table and that he is willing to discuss something in this regard.  I'm happy to hear that we can at least have a discussion with the governor on this issue," says Assemblywoman Addie Russell.

Russell says she expects to head to Albany on Tuesday.  She hopes to extend a "true" millionaires' tax.

"It makes sense to extend a tax on some of the highest income earners in this state, folks that earn a million dollars or more," Russell said.

Not everyone agrees.  Assemblyman Ken Blankenbush says he's willing to consider changes to the tax code.

"If he wants to talk about changes in the tax code, maybe changes in the brackets and maybe lower income tax for the lower income to middle class, and then work out a different kind of a tax code . . . I would be in favor of taking a look at that," says Blankenbush.

But says extending the millionaires' tax is not the way to go, Blankenbush said

"I believe that the millionaire's tax, or what I call the success tax, isn't going to lower taxes for the middle class and the lower-income, it's going to be put into a general fund which doesn't even guarantee that it's going to be spent on education," adds Blankenbush.