If Democrats attempt to ram through a reconciliation bill by simple majority vote in the Senate, then the GOP can offer an unlimited series of amendments. Federal law says so clearly and unambiguously: "a motion to strike a provision shall always be in order." That's from 2 USC 641(d)(2).
Democrats are now threatening to amend this clear provision of federal law by a simple majority vote, which would be as nuclear as anything the Senate has ever done. Ruth Marcus of the Washington Post explains:
If Democrats choose, as seems inevitable, to try to pass changes to the health-care plan under the rules of reconciliation, only a majority vote will be required. But that's not the nuclear option, despite some Republican rhetoric to that effect. Under reconciliation procedures, Republicans could not filibuster the measure. But they could offer amendments. Unlimited amendments. Senate Democrats already have the historical records handy: 58 votes on the Contract With America cuts in 1995, and 44 votes on the Bush tax cuts.
Here is where the nuclear move comes in. If Republicans exercise their prerogative to propose amendments and show no signs of quitting, Democrats could use the nuclear option to make them stop. After some number of amendments, the majority leader or another Democrat could seek a ruling that the amendments had become dilatory and abusive. If the parliamentarian were to disagree, whoever is chairing the Senate at that time could overrule him. Republicans could appeal that ruling. Democrats could move to table the appeal, essentially upholding the decision that no additional amendments would be allowed. And -- this is the important part -- that would only require a majority vote.
If this happens, then basically the U.S. Senate will come to a grinding halt, and the federal government will be paralyzed indefinitely. All this, in the name of legislation that Americans overwhelmingly oppose, and that cannot garner a 60-vote supermajority in the Senate.