As they prepare to reconcile a massive economic stimulus bill, both House and Senate Democrats and the White House are trying to figure out just how far they can push three Senate Republicans without losing their votes.

Senate Majority Leader Harry Reid (D-Nev.) can’t pass his chamber’s $820 billion-plus bill without Sens. Susan Collins (Maine), Arlen Specter (Pa.) and Olympia Snowe (Maine). Nor can he pass a looming House-Senate conference report without them, given the 60-vote threshold he must overcome to beat back a GOP-led filibuster.

That’s why Reid and the 57 other members of the Democratic caucus reluctantly agreed last week to a bipartisan demand to strike $108 billion from the Senate measure.

Still, Democrats have apparently decided to test their luck by trying to restore much of the education money they gave up in order to secure those Republican votes.

For example, Congressional Democrats and the White House are trying to figure out how to get $16 billion in school construction funding back in the measure without tinkering with the overall cost.

“I don’t think they should have a problem with it if the overall number stays in the ballpark,” posited one senior Senate Democratic aide.

The aide said Collins, Snowe and Specter might have a hard time voting against the measure once it comes back from conference committee.

“They’re invested in it now,” another Senate Democratic aide said. “It’s definitely a tough needle to thread, but I think it can be threaded in a way to bring everybody along.”

Even President Barack Obama appears interested in restoring some of the cuts he pushed Senate Democrats to accept, if you believe his chief economic adviser, Larry Summers.

“There’s no question what we’ve got to do is go after support for education. And there are huge problems facing state and local governments,” Summers said Sunday on ABC’s “This Week.” “We’re going to have to try to come together in the conference, and the president is certainly going to be active in sharing his views as that process goes on.”

The calculation Democrats appear to be making is that the three Senate GOP moderates would not want to be responsible for a filibuster of the bill, particularly if that filibuster is over funding for schools across America.

And they may be right.

However, Republicans specifically singled out school construction money in the Senate bill because they said they believed it is not the job of the federal government to perform that task.

Collins told CNN this weekend that she would be scouring the House-Senate compromise for radical changes to the deal she hammered out with Democratic Sen. Ben Nelson (Neb.) and Democratic-leaning Sen. Independent Joe Lieberman (Conn.).

“If the bill comes back from the conference committee with a lot of wasteful spending reinserted, or comes back in excess of $800 billion, it will not have my support. So I hope that my colleagues will follow the outlines of the compromise that we negotiated this week. That is important to me. I don’t want to see a bloated, overly expensive bill,” Collins said.

Plus, there doesn’t appear to be any other Republican Senate votes in play.

Minority Leader Mitch McConnell (R-Ky.) said Collins, Specter and Snowe will likely be the only GOP Senators to support the measure during final passage today. They were the only ones to support a crucial test vote Monday night, which succeeded on a 61-36 vote and allowed Democrats to bring debate on the bill to a close.

“I’m sure that they believe that they’ve improved the bill. I don’t think they’ve improved it enough to garner additional Republican support in the Senate,” McConnell said at a press conference Monday.

Another senior Senate Democratic aide said the alterations to the stimulus bill in any conference committee would have to be delicately made because it was not just Republicans that balked at the bill’s original funding scheme.

It’s a high-stakes gamble,” one senior Senate Democratic aide said.

“You have to take Sen. Nelson and others at their word that they would have voted against this thing.”

The aide added that House Democrats are likely going to have to swallow some difficult cuts to programs they championed in the House-passed measure, regardless of whether some education or state funding is restored.

After all, the aide said, Speaker Nancy Pelosi (D-Calif.) can pass almost anything without GOP votes. That doesn’t fly in a Senate where Reid has only 58 Members but needs 60 to pass controversial legislation.

“Steamrolling Republicans is not an option over here,” the senior Senate Democratic aide noted.

House Democrats said they are cognizant that they can’t push so hard that they jeopardize a fragile Senate coalition. “What’s critical here is getting something to sign. What is the best bill we could get?” one House Democratic leadership aide said.

The decision could come down to whether to make room in the bill for more spending by eliminating the Senate’s $70 billion fix for the alternative minimum tax.

But the question remains whether key Republican voters would balk at that sleight of hand.

Still, House Democrats are likely to push hard on their priorities, which include school construction and more aid to state and local governments.

“That’s about saving firefighters and teachers,” the House Democratic leadership aide said.

The aide noted that Obama has been vigorously defending pieces of the House package since he gave a speech to House Democrats Thursday night.

The Democratic Congressional Campaign Committee, meanwhile, was launching a second wave of attacks against House Republicans and noting a new Gallup Poll that showed the GOP’s handling of the crisis to be extremely unpopular.

Republicans continue to propose a package that relies entirely on tax cuts rather than the mix of tax cuts and spending in the Democratic package.