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.

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 AlexanderAndrew (Lamar) Lamar AlexanderOn The Money — Sponsored by Prudential — Supreme Court allows states to collect sales taxes from online retailers | Judge finds consumer bureau structure unconstitutional | Banks clear Fed stress tests Supreme Court rules states can require online sellers to collect sales tax 13 GOP senators ask administration to pause separation of immigrant families MORE (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 FoxxVirginia Ann FoxxTaxpayers and consumers alike should cheer defeat of the farm bill A call to service without debt Congress, pass the PROSPER Act for federal student aid reform MORE (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.