Members of the U.S. Senate voted early Tuesday morning to approve a last-minute plan to avert income tax hikes on all but the richest Americans and stall painful spending cuts as part of a compromise to stave off the fiscal cliff threatening the country.

The House of Representatives can vote on the measure as early as Tuesday, thereby limiting the economic damage even though the fiscal cliff deadline passed at midnight on New Years Eve.

The Senate vote came at 2 a.m. EST, hours after federal lawmakers reached at least part of an agreement to counteract the fiscal cliff that would bring automatic tax increases to all Americans on Tuesday.

President Obama called the tax agreement the most important part of the deal.

Some of the key parts of the agreement included extending the expiring Bush-era tax rates for individuals making $400,000 a year or less and couples making $450,000 a year or less, and extending unemployment insurance and tax credits for tuition costs, families with kids, and clean energy companies.

There is also an agreement to keep the controversial estate tax at the current level, rather than raising it.

"I've said all along that our most important priority is to protect middle class families," said Senate Majority Leader Harry Reid. "This legislation does that."

"This shouldn't the model for how we do things around here, but I think that we can say that we've done some good for the country," said Senate Minority Leader Mitch McConnell.