But even if the bill does get a better score, Valliere said it would never pass the Senate, which is drafting its own bill. "Right now, both sides are pretty well dug in. I think this would never make it through the Senate," said Valliere. "The only thing the market cares about is the tax bill. There are some signs of movement there." Health care has been set as a priority ahead of the tax bill, but Valliere said House Ways and Means Chairman Kevin Brady indicated he has a blueprint ready to discuss on tax reform after the Memorial Day holiday.
The health care bill scoring has been important for markets since if it fails and requires a new House vote, traders will take that as another delay.
"It gums up the works. It's another distraction and it's another reminder of things that are not getting done," said Kohli.
The government releases data on oil and gasoline inventories at 10:30 a.m. ET Wednesday. Oil prices could be volatile ahead of Thursday's OPEC meeting, where ministers are expected to approve a plan to extend production cuts by nine months.
There are also a few Fed speeches, including Dallas Fed President Robert Kaplan speaking in Toronto at 6 p.m. ET and Minneapolis Fed President Neel Kashkari, speaking at 6:30 p.m. ET.
On the budget front, Mick Mulvaney, director of the Office of Management and Budget, appears before the House Budget Committee at 9:30 am. Treasury Secretary Steven Mnuchin appears before the House Ways and Means Committee at 2 p.m.
House Speaker Paul Ryan holds a briefing at 11:30 a.m. with other GOP House leaders.
There are also earnings, including retailers Lowe's, Tiffany, and Chico's FAS. Advanced Auto parsts, and JA Solar also report before the bell. Williams-Sonoma, PVH, Pure Storoge and HP, report after the bell.
President Donald Trump continues his overseas trip, arriving in Italy Tuesday. He is scheduled to meet with NATO members and attend the G-7 starting Friday.
Watch: Small business concerned about health care