Will Obama sign a health care reform bill that will increase the federal deficit?

Obama said last week that he would not sign a health care bill if it would increase the federal deficit by one dime. Yesterday, Phil Gingery a Republican representative from Georgia who is a medical doctor offered an amendment to the House bill that required the bill to have a clause that the bill could not increase the federal deficit. It was defeated along party lines by the Democrats. Obama, who is a Democrat, said he would sign no such legislation. Will Obama cave to the Democrats in Congress, or will he be true to his word and veto the legislation if the amendment is not in there?