Trying to quell a conservative uproar over his health care agenda, President Barack Obama has proposed barring illegal immigrants from a possible government-arranged health insurance marketplace -- even if the immigrants pay with their own money. The move has surprised some of Obama's fellow Democrats and infuriated immigrant advocates, who on Tuesday attacked the position as political pandering and bad policy. The White House revealed its stance Friday, after a renewed debate over illegal immigration that was triggered when Rep. Joe Wilson, R-S.C., heckled Obama on the issue during the president's televised address to Congress. Wilson yelled out, 'You lie!' when Obama said that illegal immigrants would receive no benefit from his healthcare proposals. But some on the political left say that the White House -- wary of more damaging battles with the right -- has given in to Wilson and other conservatives. Wilson 'acted like a buffoon, and everybody criticized him -- but then at the end of the day he sort of got his way,' said Brent Wilkes, national executive director of the League of United Latin American Citizens. 'It rewards bullying in a way that begets more bullying,' said Frank Sharry, who directs the pro-immigrant group America's Voice and has been advising the White House and congressional Democrats on broader immigration issues. After a sharply partisan debate Tuesday, the House voted 240-179 to formally rebuke Wilson for his outburst. A White House official said Obama's stance barring undocumented immigrants from participating in the insurance marketplace did not reflect a change of heart after Wilson's outburst -- only that the specific question had just come up in recent days. 'The president has been clear since the campaign that he does not intend for health insurance reform to cover undocumented immigrants,' said the official, who spoke on the condition of anonymity while discussing official White House policy. But several White House allies said Tuesday the new policy was a shift designed to position Obama to the right of his critics. Rep. Luis Gutierrez, D-Ill., an early Obama ally, said Tuesday that members of the Congressional Hispanic Caucus were reevaluating their support for the healthcare bill. Wilson's outburst, Gutierrez said, was 'said in a mean, ugly way. And what the president did was create an even meaner, uglier public policy to accompany it.' Congress is working on plans to give low- and moderate-income people subsidies to buy health insurance in an effort to reduce the number of uninsured in the country. None of the measures would allow illegal immigrants to receive subsidies. Obama's proposal, circulated in an e-mail to reporters, would go further, barring undocumented immigrants from an insurance marketplace designed to make it easier for consumers to find coverage. As they can today, undocumented immigrants still could buy insurance in the private market. But the White House e-mail noted that if the Democratic legislation passed, private insurers could be expected to sell more insurance through the so-called exchange and less coverage outside of it, leaving the private market to shrink over time. The White House also has embraced a verification system to validate that people buying insurance were in the country legally. That idea had been rejected by House Democrats, who cited studies showing that such systems were costly and prone to mistakes. The White House has not, however, proposed changing the law that requires emergency rooms to treat people who need care, including illegal immigrants. Immigrant advocates said Tuesday that the insurance issue could be a political headache for the White House if members of the Congressional Hispanic Caucus, after hearing from their constituents, feel pressured to vote against the healthcare legislation. Some said they intended to organize activists in the coming days to push the White House and Democratic leaders to make the bill more favorable to immigrants. Obama's policy statement, some activists said, was motivated by politics -- an effort to build credibility with conservatives and defuse criticism that the president was soft on illegal immigration. Hispanic leaders and immigrant advocates aired their concerns during a Monday meeting at the White House. Administration officials explained that the insurance coverage restriction was needed for the sake of clarity, according to several meeting participants. One official, White House Deputy Chief of Staff Jim Messina, assured the group that Obama supported allowing legal immigrants to participate in the insurance exchange. Advocates said they presumed that meant legal immigrants would be eligible for subsidies. Conservative critics have said that allowing illegal immigrants to participate in a government-run system rewarded lawbreakers. Moreover, they said, any ban on subsidies to illegal immigrants would be ineffective without an enforcement mechanism, such as requiring consumers to show they were in the country legally. But others have argued that imposing hurdles on illegal immigrants who want to buy insurance forces those people to hospital emergency rooms and raises taxpayer costs. And because illegal immigrants tend to be younger and more fit, their participation in insurance risk pools could actually drive down costs. Leighton Ku, a health policy professor at George Washington University, said immigrants' health care costs about half as much as citizens' care. 'They're low-risk people,' Ku said. 'It's advantageous to have low-risk people in insurance pools.' It was unclear how the policy would affect families in which parents were in the country illegally and the children were citizens, or how it would affect illegal immigrants who get their insurance through their employers, who might choose to participate in the new insurance exchange. Experts said Tuesday that the dust-up over immigration amid the broader healthcare fight underscored the political challenges that await the White House later this fall and next year, when Obama has said he hoped to overhaul the immigration system. Obama has said he supports creating a pathway to citizenship for the estimated 12 million illegal immigrants currently living in the United States. But some say that his new restrictive policy violates the spirit of that old pledge. 'It's a contradiction in terms,' Gutierrez said, 'to say that people live in the shadows, that they live in a constant state of exploitation -- and then to push public policy that simply pushes them further into the shadows, further onto the periphery of society.' 