Speaker John Boehner leaves his office Tuesday and walks to the House floor to deliver remarks about negotiations with President Obama on the fiscal cliff.

The offer from the speaker follows his remarks on the House floor in which he said the White House was slow-walking the process. Unless a deal is reached, automatic across-the-board spending cuts and sweeping tax increases are scheduled to go into effect at the first of the year.

The back and forth over the "fiscal cliff" continues: House Speaker John Boehner sent a new counterproposal to the White House on Tuesday that, according to a spokesman for the speaker, aims to "achieve tax and entitlement reform to solve our looming debt crisis and create more American jobs."

Tuesday's offer from Boehner follows his remarks on the House floor in which he called on President Obama to identify what spending cuts the White House will accept as part of a "balanced approach" toward a deal.

"The longer the White House slow-walks this process, the closer our economy gets to the fiscal cliff," Boehner said.

The White House responded by outlining Obama's proposals, including cutting $340 million from Medicare over a decade, and $250 billion from other programs.

The main battle between the two sides is over taxes. Obama wants to restore the Bush-era tax cuts for those with high incomes, but Republicans say that would hurt the economy.

The Associated Press reported Tuesday that Obama and Boehner have exchanged at least partial proposals in the past two days. The two men met Sunday at the White House, but gave few details about what was discussed to avert automatic across-the-board spending cuts and sweeping tax increases that are scheduled to go into effect at the first of the year – unless a budget deal is reached.

NPR's Marylin Geewax and Greg Henderson have reported on the timeline of what would happen if no deal is struck. Here's an excerpt from their story:

"But resolving the mess is extremely important: Without a solution, every person who gets a paycheck or has investments will see his or her taxes rise.

"And if the stalemate were to linger deep into the new year, many people could see their jobs disappear. The nonpartisan Congressional Budget Office says that if President Obama and lawmakers fail to reach an agreement, the U.S. unemployment rate later in 2013 could rise to 9 percent, from the current 7.7 percent."

Senate Majority Leader Harry Reid of Nevada said Tuesday that a deal was unlikely by Christmas, blaming Republicans for the lack of progress.

Update at 6:31 p.m. ET Obama, Boehner Talk

NPR's Scott Horsley is reporting that Obama spoke late Tuesday by telephone with Boehner.

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