The two biggest labor organizations in the country are on board with the House passing the Senate version of healthcare reform, as long as changes are made through a separate process.

Officials from both the AFL-CIO and the SEIU said they want the House to pass the Senate bill in its current form, but only if Democratic leaders agree to carve out changes in the bill that could be passed separately, perhaps through budget reconciliation.

In particular, labor wants an adjustment to the so-called "Cadillac tax" to make sure it doesn't detract from the insurance policies that unions have negotiated for their members.

It would be relatively easy to modify that measure using a 51-vote budget reconciliation measure since the tax directly affects government revenue.

"The House should pass the Senate's health insurance reform bill - with an agreement that it will be fixed, fixed right, and fixed right away through a parallel process," Andy Stern, president of SEIU, wrote today in the Huffington Post.

A spokesperson for the AFL-CIO said that they're on board with that proposal.

Of course, that strategy depends on the House being able to pass the Senate bill as it currently stands. The lower chamber must pass the exact same bill in order to avoid another supermajority vote in the Senate.

Failing that, Democrats would either have to convince at least one Republican to support reform or use budget reconciliation to pass the entire legislation. The latter option would be daunting, since Republicans could launch procedural challenges to passing portions of the bill that don't directly affect government spending or revenue.