(CNN) – As proposals and plans fly between Capitol Hill and the White House, House Speaker John Boehner says negotiators are working at an increased pace to avoid the year-end fiscal cliff after Friday's deadly massacre in Connecticut.
Asked Tuesday whether the school shooting – which left 26 people dead, including 20 children – had created a greater urgency in striking a deal to avoid tax hikes and spending cuts, Boehner said it had.
"I think both sides would agree to that," the speaker said. "This is a difficult time for Americans. That's why we continue to have conversations with the White House, and continue to hope that we have an agreement. It's not a time to put Americans through more stress."
Asked a similar question at Monday's White House press briefing, President Barack Obama's press secretary Jay Carney said the shooting reminded people "what matters most."
"And I think one of the reasons why it would be such a good thing if an agreement could be reached on these fiscal and budget issues, is that it would send a signal that Washington can function and that compromise can happen," Carney said, saying Americans were yearning for cooperation between Republicans and Democrats.
"I hope that whatever the issue is, that we can come together and respond to that call and that desire. I know that's how the president feels," Carney said.
Boehner and Carney's remarks come amid a flurry of action on fiscal cliff negotiations, though it remains unclear whether congressional Republicans and the White House are any closer to reaching a deal. President Barack Obama's latest offer, which came Monday, contained concessions on tax increases and spending cuts, according to a source familiar with the discussions.
Obama's latest proposal brought the two sides billions of dollars closer, but also generated protests from some in the Democratic base because it included some benefit cuts in entitlement programs such as Social Security, Medicare and Medicaid.
Boehner on Tuesday proposed letting tax rates go up on income above $1 million as a short-term step to avoid some of the fiscal cliff while continuing to negotiate a broader deal with the president.
Democratic leaders immediately rejected Boehner's move, saying the focus of the incremental negotiations should be a comprehensive deficit reduction agreement.
CNN's Tom Cohen contributed to this report.