Ron Brownstein has an interesting column in National Journal arguing that the Senate health care bill makes a serious effort to curb costs. This longer piece on the Atlantic website, "A Milestone in the Health Care Journey" is also well worth reading.
Though I agree with much of what Ron says, and if I were a senator would vote for this bill rather than no bill, it depends what you mean by a serious effort to curb costs.
Certainly, the Senate measure is better on cost control than the House bill with which it will have to be merged. (For background, see this earlier piece by David Leonhardt, "Falling far Short of Reform", which compares the House bill with the Senate bill's precursor from the Senate finance committee; this Brookings analysis of the finance committee plan, which checks off ideas for bending the curve on health costs; and especially this newer piece by Leonhardt on the current Senate plan, "Budget hawks have a menu of options".)
As Brownstein says, the Senate bill adopts four principles advanced by a non-partisan group of health economists in a recent letter to the White House: deficit neutrality, a tax on expensive insurance plans, a Medicare commission to suggest ways of improving quality and value, and delivery system reforms.