The second one would impose a stiffer arms embargo and sanctions against human rights violators and those who violate cease-fire pacts in Darfur, in the west of Sudan.
Russia and China, which have veto power, as well as Algeria and possibly other nations object to some of these measures.
The third resolution would deal with where to try those responsible for heinous crimes in Darfur. The United States rejects the new International Criminal Court in The Hague, which most council members support, and has proposed a new U.N.-African Union tribunal, which few nations back.
To complicate issues, Nigeria, president of the African Union, has suggested a special panel to hear cases and foster reconciliation. Sudan approves of this plan but its details are still vague.
"The United States has run out of patience on Sudan and has circulated three draft resolutions: one of resolutions, one on peacekeeping, one on sanctions and one to provide for measures to end impunity," said Anne Patterson, the acting ambassador.
"It is clear there is very broad support for the peacekeeping resolution and that is very very critical because it will strengthen the new government in Sudan and get more boots on the ground," she told reporters.
Patterson wants a vote on Wednesday or Thursday in what promises to be gripping diplomatic theater if two of the resolutions encounter successive vetoes.
Tens of thousands have been killed in the two-year-old rebellion in Darfur, with thousands dying every month in miserable camps which house the almost 2 million people who have fled their homes. Arab militia, known locally as Janjaweed, have begun to threaten relief workers.