Republicans oppose any kind of increase in tax rates, and Boehner suffered the political indignity last week of offering a compromise -- a $1 million threshold for the higher rates to kick in -- that his GOP colleagues refused to support because it raised taxes and had no chance of passing the Senate.
Last Friday, the president proposed the scaled-back agreement that included his call for extending tax cuts on households with incomes up to $250,000, as well as an extension of unemployment insurance.
Reid and Democrats reject the GOP proposals, which would extend all the Bush tax cuts and revamp the spending cuts of the fiscal cliff, calling them insufficient and saying they would shift too much deficit reduction burden on the middle class.
One possibility is the fiscal cliff takes effect and taxes go up in January, then Congress steps in to bring tax rates back down for at least some people -- allowing them to say they're lowering taxes, even if rates for top income brackets are higher in 2013 than they were in 2012.
Obama and Democrats have leverage, based on the president's re-election last month and Democratic gains in the House and Senate in the new Congress. In addition, polls consistently show majority support for Obama's position on taxes, and Democrats insist the House would pass the president's plan with Democrats joined by some Republicans if Boehner allowed a vote on it.
However, anti-tax crusader Grover Norquist has vowed to back primary challenges against Republicans who violate his widely signed pledge not to raise taxes. Even if a deal is reached, Norquist predicts budget showdowns will continue every time the government needs more money to operate.
"There the Republicans have a lot of clout because they can say we'll let you run the government for the next month, but you've got to make these reforms," he said this week.
On Wednesday, Treasury Secretary Timothy Geithner told Congress the government would reach its borrowing limit at year's end, but could take steps to create what he called "headroom" for two months or so.
However, Geithner said uncertainty about the fiscal cliff and deficit negotiations make it hard to predict precisely how long government measures to address the situation will last.
The possibility of a fiscal cliff was set in motion over the past two years as a way to force action on mounting government debt.
Now, legislators risk looking politically cynical by seeking to weaken the measures enacted to try to force them to confront tough questions regarding deficit reduction, such as changes to government programs like Social Security, Medicare and Medicaid.
The two sides seemingly had made progress early last week on forging a $2 trillion deficit reduction deal that included new revenue sought by Obama and spending cuts and entitlement changes desired by Boehner.
Obama's latest offer set $400,000 as the income threshold for a tax rate increase, up from his original plan of $250,000. It also had a new formula for the consumer price index -- called chained CPI -- that wraps in new assumptions on consumer habits in response to rising prices, such as seeking cheaper alternatives, and would result in smaller benefit increases.
Statistics supplied by opponents say the change would mean Social Security recipients would get $6,000 less in benefits over the first 15 years of chained CPI. Liberal groups have openly challenged the plan, calling it a betrayal of senior citizens who contributed all their lives for their benefits.
Boehner appeared to move on increased tax revenue, including higher rates on top income brackets and eliminating deductions and loopholes. But his inability to rally all House Republicans behind his plan last week raised questions about his role and what comes next.