"I know how important the supplemental relief is to those affected by Hurricane Sandy, but I believe we can provide that relief while finding ways to pay for it, rather than adding to the nation’s ballooning deficit," Mulvaney said Friday. "Indeed, if we cannot come together under these tragic circumstances to find a way to pay for this relief, do we seriously believe we will have the political will to ever balance the budget?"

As of Friday morning, Mulvaney's were the only amendments filed to the Sandy relief bill, although the deadline for filing is today. The Rules Committee has planned a meeting at 5 p.m. Monday, when it will decide what amendments to make in order.

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The amendments will likely be seen as controversial, especially among Democrats and even many Republicans who have argued that emergency disaster aid does not have to be offset. For that reason, Mulvaney's amendments are expected to face tough sledding in the House even if they are made in order.

If recent House votes are any guide, they are likely to be opposed by nearly every Democrat, and possibly by more than half of the Republican caucus. That combination would easily be enough to sink Mulvaney's proposals.

Mulvaney's first amendment would offset the new spending with a 1.63 percent cut to all discretionary programs in the federal budget. This proposal is co-sponsored by Reps. Jeff Duncan (R-S.C.), Cynthia LummisCynthia Marie LummisLiz Cheney leads GOP field by 20 points in potential Wyoming Senate race: poll Liz Cheney and Rand Paul extend war of words Pressure rises on Cheney to make decision MORE (R-Wyo.) and Tom McClintock (R-Calif.).

A second amendment from Mulvaney would offset the $17 billion by ending transit subsidies for federal workers, eliminating the Agriculture Department's direct payments to farmers, and prohibiting any further TARP spending. That proposal is co-sponsored by Reps. Steve Scalise (R-La.) and McClintock.

Mulvaney also filed a third amendment requiring periodic reports from agencies that would have to identify the funds requested and received, describe how they were used, and include a certification that they were used appropriately. This amendment is sponsored by Reps. Scott GarrettErnest (Scott) Scott GarrettBiz groups take victory lap on Ex-Im Bank Export-Import Bank back to full strength after Senate confirmations Manufacturers support Reed to helm Ex-Im Bank MORE (R-N.J.) and McClintock.

Aside from the main bill and possible amendments, the House is expected to consider a major amendment from Rep. Scott Garrett (R-N.J.) that would add another $33.7 billion in Sandy relief funding. Among other things, that amendment would provide nearly $20 billion for the repair of roads and bridges.