Senate Finance Chairman Max Baucus (D-Mont.) late Monday said progress was made toward Democratic unity on his $856 billion health care reform package, but signaled work would continue on that front even after the legislative markup begins Tuesday morning.

Baucus and Finance Democrats met privately Monday evening to address lingering concerns about affordability and how the mandates to purchase health insurance in the committee’s bill would hit middle- and lower-class Americans. Baucus on Tuesday will introduce a modified bill that attempts to mollify concerns affecting the current proposal’s deficit neutrality.

“It was a very good discussion,— Baucus said following the meeting. “We’ve come a long, long way.—

Despite 564 amendments being filed against the bill, Baucus predicted the markup would finish by week’s end, although he declined to predict an exact day.

Baucus said his modified proposal would lower the penalty on individuals and families who do not purchase health insurance, in an effort to address concerns about affordability. Baucus would not reveal by how much the levies would be reduced. The fines in Baucus’ original proposal run as high as $950 per individual and $3,800 per family.