Dozens of House Republicans proposed several bills on Monday that would delay ObamaCare or allow people to keep their current health insurance plans.

The bills are the latest reaction to the dysfunctional website that may not work for another month or more, even as health plans around the country are being canceled. But as of Tuesday, House GOP leaders had not indicated that any of them would come up for a vote.

One of the proposals, from House Energy & Commerce Committee Chairman Fred UptonFrederick (Fred) Stephen UptonLive coverage: Zuckerberg faces second day on Capitol Hill Russian attacks on energy grid spark alarm Bipartisan 'No Labels' group aims to protect moderates in primary fights MORE (R-Mich.) and more than two dozen Republicans, would authorize insurance providers to continue to offer individual health plans that would otherwise have to be canceled under ObamaCare. The Keep Your Health Plan Act, H.R. 3350, would also ensure that anyone using their old healthcare plan would not face a penalty under ObamaCare.

"Despite the president's repeated promise of 'if you like your plan, you can keep it,' many Americans are now learning the sad reality that their current plan will no longer exist beginning on Jan. 1," Upton said Monday. "Instead they are forced to purchase healthcare that they cannot afford through a system that does not even work, and that's just not fair."

Rep. Trey RadelHenry (Trey) Jude RadelEx-GOP rep: Ryan avoids Speakership to protect shot at higher office 2014's top scandals After yearlong absence, ex-congressman makes Twitter return MORE (R-Fla.) and more than a dozen Republicans proposed the Delay Until Fully Functional Act, H.R. 3359. That bill would delay implementation of ObamaCare until the Government Accountability Office certifies that the website is working.

Radel's bill is a companion to one offered by Sen. Marco Rubio (R-Fla.).

"The president has already given big business and corporations an exemption from his signature law, it only seems fair to give you and your family a break from the fine as well," Radel said. "The Rubio-Radel bill ensures the ObamaCare fine will be delayed until the administration can show and all other sign up options are fully functional."

"It is unacceptable that Americans will soon be forced to pay a fine for not purchasing insurance when the very websites they are supposed to use for purchasing it have been rendered useless from numerous glitches and technical errors," Rubio added.

Rep. Luke Messer (R-Ind.) proposed a similar bill, H.R. 3358, which would exempt people from the individual mandate in states where the healthcare website is not working.

Rep. Joe BartonJoe Linus BartonThe Hill’s Morning Report: Michael Cohen’s big day in court 'Diamond & Silk' offer chance for bipartisan push back on social media censorship Republicans express doubts that Ryan can stay on as Speaker MORE (R-Texas) and a dozen other Republicans proposed H.R. 3348, which would make the individual health insurance mandate voluntary in 2014. Barton said on the House floor Monday that given that people's insurance plans are being canceled and the cost of new plans is higher than expected, people should be allowed to opt out.

"If it is as good as the president says it is, people will join and get the benefits from it," Barton said. "If, on the other hand, they can't get the software fixed, the policy mandates are unsustainable, and the costs are too high, the American people will choose not to participate.

"It is a simple bill that makes participation voluntary by suspending the tax for non-participation."