After Senate Republicans agreed to open debate Tuesday to overhaul the Affordable Care Act, they quickly shot down what was once their&nbsp;leading&nbsp;proposal&nbsp;for repealing and replacing&nbsp;Obamacare.Republicans rejected their revised bill, the Better Care Reconciliation Act, despite having added&nbsp;a provision from Sen. Ted Cruz (R-Texas)&nbsp;favored by conservatives and another from Sen. Rob Portman (R-Ohio) to court centrists worried about Medicaid cuts.It failed 43 to 57, not reaching the 60-vote threshold needed to advance. Nine Republicans voted against it.President Trump warned Republicans during a rally in Youngstown, Ohio, late Tuesday that they needed to act after having promised for seven years to repeal and replace the healthcare law."Now they must keep their promise," Trump said.&nbsp;"Any senator who votes against repeal-and-replace is telling America that they are fine with the Obamacare nightmare, and I predict they will have a lot of problems."But dispatching with the bill that was once considered to be the GOP's best chances at fulfilling their campaign promise to end the law now leaves Republicans with few options.Senate Majority Leader Mitch McConnell (R-Ky.) promised senators a robust debate if they agreed earlier Tuesday to vote on the motion to open the legislative process.Typically, that means round-the-clock voting, with senators able to offer unlimited amendments as part of the special budget process Republicans are using for the healthcare debate.&nbsp;More votes are set for Wednesday.But with Democrats preferring to fix the healthcare law rather than end it, Republicans are largely left on their own. Even though most votes will require only 51 votes for passage, the 52-seat Republican majority is split on key healthcare issues, making various GOP proposals unable to win support.Instead, Republicans&nbsp;may settle on an idea leaders floated this week -- what's being called "skinny repeal" -- a measure that would end just a few key parts of Obamacare. It would repeal the law's mandate&nbsp;that all Americans carry insurance and that bigger employers must provide it to their workers, or pay fines. The skinny repeal could also end some taxes, including one on medical device makers.Passage of the skinny repeal would be far from the Republican promise to repeal Obamacare&nbsp;completely and replace it with another healthcare program. It would also need approval by the House, where Republicans have passed a more sweeping repeal and replacement bill.