The White House said Tuesday that President Obama would veto a House bill that would exempt people from penalties if they purchased health insurance through Obamacare co-ops, and then lost their plan because the co-op failed.

The bill, sponsored by Rep. Adrian Smith, R-Neb., would say the law's individual mandate tax penalty would not apply to those who unexpectedly lost their health insurance through no fault of their own but because Consumer Oriented and Operated Plans, or Co-ops, created under the law, failed or are in the process of closing.

The Office of Management and Budget issued a statement saying Obama would veto the bill, and said the Obama administration has already reached out to people who lose their plans to help them transition to other plans. It also said people can already qualify under the law for exemptions to the individual mandate penalties.

"These options are available to all consumers in these circumstances, not just those enrolled in coverage through co-ops," the OMB said.

OMB also argued that the bill would weaken the "individual responsibility provision," which in turn would "increase insurance premiums and decrease the number of Americans with coverage." For those reasons, the bill would be a "step in the wrong direction, because it would create a precedent that undermines a key part of the law and would do nothing to help middle-class families obtain affordable health care."

Smith and other Republicans have said the bill would provide some solace for Americans who have lost their coverage midyear because the Obamacare-created co-ops failed.

"It is only fair that we reduce the impact further for these families and ensure that if any other co-ops close that families struggling to make an unexpected decision about health insurance midyear don't have individual mandate penalties to worry about," he said after the bill passed the Ways and Means Committee in early September.

Rep. Pat Tiberi, R-Ohio, who chairs the Ways and Means health subcommittee, said the problem has harmed nearly 22,000 people in his state who signed up with InHealth co-op.

"Thirty-one percent of American counties have one provider of health insurance, they don't have choices," he said earlier this month.

"In Ohio, if you had InHealth, in some of my countries not only did you wake up one day and have no health insurance – zero, none – you lost your doctor," he said. "Now you go look at the plans, there's one. One plan. You lose your health care, you lose your doctor, and now you're going to get penalized."