(CNN) – It's down to the wire for President Obama's health care overhaul.

The key to getting reform done is the thirty seven Democratic congressmen and women who are wavering or voted "no" the first time. Each is being heavily courted by the president and House leaders.

One Democrat not on that list, but still on the fence, is Virginia Rep. Gerry Connolly. You would think the White House would have reached out, but you'd be wrong. Our Jim Acosta caught up with the congressman for this report.

[cnn-photo-caption image= http://i.cdn.turner.com/cnn/2010/POLITICS/03/15/health.care.next/t1larg.senate.gi.jpg caption="To pass the Senate bill or not? Either way, House Democrats face risks."]

By Kristi Keck, CNN

(CNN) - House Democrats wary of the Senate health care bill find themselves in a quandary.

Now that the Senate parliamentarian has made clear to Democrats that they won't be able to take the path they had considered to get a health care bill passed, they must ask themselves: If we vote for the Senate's bill, do we trust the senators to make the changes they say they will?

"If the House is going to do this, they are going to have to vote for the Senate bill, holding their nose and trusting that in fact they are going to go through this reconciliation process, and they are going to get the fixes that they are looking for to the legislation," said Cheryl Block, a professor of law and a budget policy expert at Washington University in St. Louis, Missouri.

Those "fixes" are a part of a package of changes to the Senate bill that President Obama proposed last month. The idea is for the House to pass the Senate bill, wait for Obama to sign it into law, and then vote separately on Obama's proposal.

The Senate no longer has the 60-seat supermajority it did when it passed its health care bill in December, so it would need to pass Obama's plan using the parliamentary shortcut known as reconciliation. FULL STORY