President Obama Monday declared that a deal to avoid massive tax increases for most Americans was “within sight” but “not done” as lawmakers scrambled just hours before their self-imposed deadline to avert the so-called fiscal cliff.

“Keep the pressure on and let’s see if we can get this thing done,” Obama said in a campaign-style speech surrounded by middle-class Americans. “They’re close — but they’re not there yet.”

Vice President Biden and Senator Minority Leader Mitch McConnell, R-Ky., have reached an agreement on tax increases for high-income people but remain stuck on how to address federal spending cuts.

Under their pact, income taxes would rise to 39.6 percent from 35 percent for individuals making $400,000 annually and couples earning $450,000 a year. The president had campaigned on raising taxes for all couples making more than $250,000 annually and Republicans had resisted all efforts to raise any income tax rates.

But here’s the sticking point: The White House and Democrats are insisting on a one-year delay in the federal sequester, which calls for tens of billions in cuts to the Pentagon and other departments in 2013 and beyond. Republicans called for just a three-month postponement in the cuts.

Neither side has budged yet.

Despite the limited time to reach a deal, the president took a jab at Congress, saying Republican lawmakers had essentially blocked the type of “grand bargain” he preferred.

“With this Congress, that was apparently too much to hope for,” Obama quipped, immediately igniting strong pushback from Republicans who are weighing whether to sign off on an agreement.

“Does [Obama] want a deal or not? Because all those jabs at Congress certainly sounded like a smack in the face to me,” Erica Elliott, spokeswoman for House Majority Whip Kevin McCarthy, R-Calif. said on her Twitter account.

And though a deal is closer to fruition, it’s hardly guaranteed that the GOP-controlled House will give its blessing to the Biden-McConnell agreement. In recent weeks, Republicans resisted a bill that would have just raised taxes on millionaires.

Obama’s partisan speech was also aimed at progressives who wanted to raise more tax dollars before the new year.

Sen. Tom Harkin, D-Iowa, said that raising the tax threshold to $450,000 a year “doesn’t sit well with this senator,” calling the framework “grossly unfair” and a “tough pill to swallow.”

Under the arrangement, the estate tax would increase from 35 percent to 40 percent for estates over $5 million. And Democrats would receive an extension in unemployment benefits, costing $30 billion.

It’s unclear whether the House and Senate will vote on the package before the clock strikes midnight. Some House Republicans said they would prefer to vote Tuesday and then make any changes retroactive.