The Senate can pass a health care bill without a single Republican vote. In fact, Democrats can afford to have some of their own members vote against health reform. The big rub is on whether to include a strong "public option" as part of the bill. A public option would allow people to have the option of buying health insurance directly from the government. The fewer Republican votes then the stronger the public option.
Bi-partisanship is a means to an end and not an end itself. The end is a health care bill that provides affordable health care for all Americans. A public option is a major component of that goal and Democrats have enough vote to get some form of public option passed. President Obama's letter made it more likely that the public option will be a strong one. There is no need for the Democrats to weaken a bill to gain GOP votes that are not needed just to satisfy the false demand of bipartisanship. Sacrificing the idea of a bipartisan bill to achieve a bill with a strong public option is a price that should be easily and willingly paid.