FALLS CHURCH, Va. – President Obama, trying to put a personal touch on “fiscal cliff” negotiations, visited a northern Virginia family’s basement apartment Thursday to press his hard line on tax rate increases for the wealthy.

“We’re in the midst of the Christmas season,” Obama said, sitting at a table in the Santana family’s Falls Church, Va., home. “I think the American people are counting on this getting solved. The closer it gets to the brink, the more stress there is going to be.”

Obama and lawmakers have until the end of the year to avert across-the-board spending cuts and tax increases. The president reiterated the firm stance he has taken in recent days, warning that he’s willing to let that economy-rattling double whammy take effect if Republicans don’t drop their opposition to higher tax rates for the wealthy.

“Just to be clear, I’m not going to sign any package that somehow prevents the top rate from going up for the folks in the top 2 percent,” Obama said.

“But I do remain optimistic that we can get something done that is good for families like this one and is good for the American economy,” Obama said.

The president’s quick trip to Virginia – just a 15-minute drive from the White House – is part of an effort to rally public support for his tax proposals. The family whose home he visited was one of many who shared a story online, at the White House’s urging, of how they would be hurt if their taxes went up at the end of the year. Obama will travel to Detroit on Monday.

Obama has said he will back spending cuts, including savings in Medicare, as part of a deal that includes the tax proposal that was a key part of his re-election bid.

Once Republicans yield on taxes, he told the Business Roundtable, “We can probably solve this in about a week; it’s not that tough.”