"They don't want to shoot the president down, that's probably why," said a political operative representing the financial services industry, who was surprised that Polis passed on commenting on the issue.
A Democratic House aide suggested that opponents of the plan are hoping they won't have to fight the president head-on to defeat it because Republicans also oppose it.
"We don't know what we'll vote on," the source said.
Members of the New Democrat Coalition are meeting Thursday, where the proposal is likely to be discussed. Reps. Chris Van Hollen (Md.) and Xavier Becerra (Calif.), who also are members of the Joint Committee on Deficit Reduction, will attend the meeting.
Obama's proposal did get the support of a key economist, Joseph Stiglitz, who voiced his approval for the plan Tuesday at a Democratic Caucus meeting.
Stiglitz argued that the jobs bill and the plan to pay for it were a "good combination," according to Rep. Henry Waxman (D-Calif.). Stiglitz said targeting tax increases to the upper-income brackets would not reduce the stimulative effect of government spending and the cutting of payroll taxes.
But Obama's proposal faces some political peril if it angers charitable organizations, universities and nonprofits that benefit from donations, particularly from wealthy benefactors.
The plan would work by limiting the overall amount of deductions that high-income earners may claim on their annual tax forms, write-offs that frequently wind up in the coffers of charities and academic institutions.
In the 111th Congress, the White House estimated the changes on deductions would bring in $318 billion over 10 years. On Monday, Lew said the changes would bring in $400 billion over 10 years.
Higher education institutions might be hit particularly hard, experts say, adding to the bleak financial situation many academic administrators already find themselves in.
Insiders say universities and charitable organizations have significant influence on Capitol Hill because of the good will their groups have engendered.
Sandra Swirski, executive director of the Alliance for Charitable Reform, a group that has opposed Obama's plan to limit deductions in the past, wasn't worried that the president's most recent proposal would gain traction this time around.
United We Dream protesters carry a mock coffin to the office of Sen. Ted Cruz, R-Texas, in the Dirksen Senate Office Building on Monday, July 21, 2014, to hold one of their "funeral services for the Republican Party" due to GOP positions on immigration. The immigration reform group visited several other Senate Republican offices to hold similar funeral services.