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(CNN) - Some 106,185 people signed up for Obamacare in its first month, a period marred by major technological problems with both the federal and state enrollment websites.
Fewer than 27,000 Americans selected an insurance plan through the federal HealthCare.gov site, which is handling enrollment for 36 states.
"Just another day in a series of mess ups in Obamacare," said House Majority Leader Eric Cantor, R-Virginia.
"Any of these numbers pale in comparison with the millions of Americans who are receiving these cancellation notices," added Cantor. "Millions of Americans are being told by their insurance companies they can no longer have the health care they need because of Obamacare."
But there are people benefiting from Obamacare, some of them from Cantor's district in Virginia.
Virginia resident Anne Maliff's son has special needs.
"His monthly medication bills, if I didn't have health insurance, would be over $1,000," Maliff told Virginia's local television station WTVR. "It certainly gives me a level of comfort I didn't have before."
"You actually have the opportunity to get affordable health care, because I currently don't have a job that offers health care," resident Sherree Wells told WTVR.
In addition, a Kaiser Family Foundation study found more than half of Virginians will be eligible for these tax credits to help them.
"There is a better way for them to benefit, and to have health care insurance that fits their needs," Cantor said. "There is a more efficient way to help those with preexisting conditions. We don't feel they ought to be denied coverage but we ought not be raising prices on people."
"What we have said is - that we would believe in the creation of high risk pools at the state level, properly and adequately fund them, and then ensure that the rates and premiums they're charged don't exceed at least 100, 150% of the market rate for insurance," said Cantor.
There is a bill in the Republican-led House that would let insurance companies continue offering plans that don't meet Obamacare standards for another year, but health care expert says this will be an administrative nightmare.
Prominent Democrats, chiefly former President Bill Clinton, and the No. 2 Democrat in the Senate, Dick Durbin, have also suggested honoring President Barack Obama's promise that Americans who like their health plan can keep it.
"If the Democrats are now saying, we ought to let people choose, we ought not be imposing higher prices on people, then yes, we certainly want to work with them," said Cantor.
The health plans negatively impacted by Obamacare are being canceled, in part, because they don't meet the standards of the President's new health care law. They are what the administration calls junk plans.
"This has been the problem all along, when President Obama thinks he knows better for families, what they need, what they can afford - that's when things go awry," said Cantor.
For more of our interview with House Majority Leader Eric Cantor, including his view on Iran negotiations, watch the video above.
CNN's Jessica Metzger contributed to this report.