Moderate Sen. Mary Landrieu (D-La.), who will not commit to supporting a motion to proceed on the Democratic leadership’s health care overhaul, is moving to align herself with Republican Sen. Olympia Snowe (Maine) as the fight heads to the floor.

Landrieu, speaking to reporters Tuesday after joining Health, Education, Labor and Pensions Chairman Tom Harkin (D-Iowa) at an event that sounded like a rally for the public insurance option, confirmed that she’s still on the fence on the motion to proceed. She reiterated her opposition to a government-run health plan. Tuesday’s event featured dozens of small-business owners — including Landrieu constituents — advocating for the Democrats’ health care agenda.

Landrieu said she favors relying on the private market to bring down costs and indicated that she supports Snowe’s proposal for a “trigger— that would only allow for a public insurance option if private insurers fail to provide affordable coverage for all. The Louisiana Senator said moderate Democrats are working with Snowe to find a way forward on health care reform.

“We are working together, not necessarily as a formal group,— Landrieu said, adding about Snowe’s trigger proposal: “That is kind of where both of us are, believing that we should reform the private market first. If the private market fails to reform or refuses to reform, then there would be a fallback position.—

Meanwhile, Harkin said he hopes the Congressional Budget Office completes its analysis of the Democrats’ health care reform bill on Tuesday. Harkin said he had hoped the CBO would finish its work last week — or at least by Monday, adding that he doesn’t know what the holdup is.

Senate Majority Leader Harry Reid (D-Nev.) forwarded a number of proposals to the CBO and plans to make a final decision about what to include in the final health care reform legislation based on the agency’s analysis. The floor debate cannot begin until the CBO completes its review and Reid makes his decision.

“Maybe today,— Harkin said. “I can’t believe it’s taking them so long.—

Reid’s office has declined this week to predict when the CBO will come back with its analysis.