House member looks to end personal data collection under ObamaCare

Fleming noted that even Consumer Reports has told people to "stay away" from the website until it is fixed, and others have raised questions about security on the site.

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Fleming's bill is just the latest idea from Republicans about how to delay the law, which is now in its fourth week of what everyone agrees has been a troubled rollout.

Earlier today, Sen. Lamar Alexander (R-Tenn.) said he's writing a bill that would require the Obama administration to provide weekly updates about enrollments and efforts to fix the site. In the afternoon, Rep. Virginia Foxx (R-N.C.) said the government should not tax anyone for failing to sign up for health insurance under the law in light of the broken website.