FALLS CHURCH, Va.  — President Barack 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 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."

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

Obama and House Speaker John Boehner spoke on the phone Wednesday, their first known conversation in nearly a week. Neither side provided details of the call, but the White House said the lines of communication with Capitol Hill Republicans were open and there had been multiple conversations between staff.

Unless the president and Republicans reach a deal, George W. Bush-era tax rates will expire on all income earners on Jan. 1. Obama wants to continue them for 98 percent of Americans, while letting them expire on the upper income earners.

If Republicans try to block that effort, Treasury Secretary Timothy Geithner said, the administration will "absolutely" let the country go over the fiscal cliff.

The size of the problem is so large it can't be solved without rates going up," he told CNBC on Wednesday.

Geithner drew a fierce response from Republicans. Sen. Orrin Hatch of Utah called his statement "stunning and irresponsible." He added, "Going over the fiscal cliff will put our economy, jobs, people's paychecks and retirement at risk, but that is what the White House wants, according to Secretary Geithner, if they don't get their way."

Economists inside and outside the government warn that failing to reach agreement on taxes and spending could land the economy back in recession.

Beyond his insistence that taxes increase on the wealthy, Obama has also warned Republicans not to inject the threat of a government default into negotiations over the fiscal cliff as a way of extracting concessions on spending cuts.

"It's not a game I will play," he said Wednesday, recalling the brinkmanship of last year in which a budget standoff pushed the Treasury to the edge of a first-ever default.

The White House reaffirmed Thursday that it did not believe the president had the authority through the 14th Amendment to raise the debt ceiling by executive order. Democrats have previously suggested Obama could take that step.

Both sides say they want a compromise, although the administration's hand in bargaining is strengthened by polls showing public support for Obama's position on taxes, as well as by his re-election last month. The president is also working to rally the public to his side and has a trip scheduled to Detroit next week.

In a concession, Republican leaders have agreed to back increased tax revenue. Yet despite defections from within the rank and file, they have so far balked at Obama's demand that rates go up on income over $200,000 for individuals and $250,000 for couples. They have also called for spending cuts and measures to slow the growth of government benefit programs. Earlier this week, they called for curbing the growth in Social Security cost-of-living increases, as well as delaying Medicare eligibility from 65 to 67, beginning in a decade.

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."

Republicans argue that they can raise about $800 billion in additional government revenue over a decade by closing loopholes and narrowing tax deductions on the wealthy, rather than raising income tax rates. They argue the rate increase would impose a particularly harmful impact on the economy and job creation at a time when the country is still struggling to recover fully from the deepest recession in decades.