WASHINGTON  Senator Ben Nelson, Democrat of Nebraska, says he is not sure he is ready to help a Democratic health care proposal clear even the most preliminary hurdle: gaining the 60 votes his party’s leaders need to open debate on the measure later this week.

Two of his fellow Democrats, Senators Mary L. Landrieu of Louisiana and Blanche Lincoln of Arkansas, are proving tough sells as well, raising the prospect that one or perhaps all three of them could scuttle the bill before the fight over it even begins on the Senate floor.

“I think what is most important for me is to take a look at what is presented on behalf of Arkansans and figure out whether it is something that really makes sense,” Mrs. Lincoln said Tuesday. “I am responsible to the people of Arkansas, and that is where I will take my direction.”

Typically routine, the procedural approval needed to begin consideration of a bill looms as anything but routine in this instance. Instead, the vote is fast becoming a test of the leadership abilities of Senator Harry Reid of Nevada, the majority leader. It will also decide at least the near-term prospects of President Obama’s top domestic priority. And it is providing a case study of the Democrats’ difficulties in managing high expectations fueled by large Congressional majorities.