Republicans seeking to shrink the size of government oppose increasing any tax rates, arguing that Obama's plan would hinder job growth because some small business owners who file personal returns would pay higher taxes under it.
While aides on both sides have been talking, no follow-up meeting between Obama and congressional leaders has been scheduled after their initial post-election discussion on November 16.
Instead, Obama met Tuesday with small business owners to launch his week of campaign-style events.
Andra Rush, who founded Rush Trucking of Wayne, Michigan, said her message to Obama was that failure to extend the tax cuts to the middle class could stall what she called new economic momentum in the country.
"I would have higher tax rates," Rush conceded, adding that it was more important for "ordinary Americans" to have more money to spend instead of paying it in taxes if everyone's rates go up.
Boehner and other influential GOP figures have declared their willingness to consider other ways to boost tax revenue as part of a broader deal that includes entitlement reforms and spending cuts.
That position undermines the no-tax-increase pledge championed by anti-tax crusader Grover Norquist, which Democrats consider to be a major impediment to a deficit reduction deal.
Republicans insist Democrats must agree to cut discretionary spending and make significant reforms to Medicare and Social Security as part of a deficit reduction deal.
However, organized labor and other elements of the Democratic base oppose any major reforms to the popular entitlement programs. While some Democratic legislators express willingness to reform Medicare and Medicaid, they reject making Social Security reform part of the fiscal cliff negotiations, saying it is self-funded and therefore doesn't add to the deficit.
A CNN/ORC International poll released Monday also showed that a solid majority of respondents -- two thirds -- supports the Democratic stance that any agreement should include a mix of spending cuts and tax increases. Of that total, Republicans favor such an approach by 52%-44%.
Another poll on Wednesday by ABC News and the Washington Post showed a strong majority favoring the Obama tax proposal to raise tax rates on the wealthy. In addition, the survey indicated most Americans oppose raising the eligibility age of Medicare, one of the possible reforms proposed by some in the deficit debate.