Action on smaller chunks of President Barack Obama’s $447 billion jobs bill will likely be delayed by weeks as Senate Democrats and the White House have yet to settle on which pieces to move first.

After Republicans and two Democrats filibustered the bill Tuesday, Democrats and the White House indicated they would break it up to bring to the floor separately.

The idea is to force Republicans to block individual items — a payroll tax cut, infrastructure spending, etc. — that have broad support. Either Democrats will try to get the GOP to crack on a smaller piece, or they can go to the public and paint the Republicans as the do-nothing party.

But Democrats heading into their weekly policy luncheon were divided over what to do next — and emerged without a plan.

Senate Majority Leader Harry Reid said Democrats need more time.

“I have had a number of meetings today, we are working very closely with the White House and my caucus, and until we have direction from my caucus, we are not going to be able to make a decision,” the Nevada Democrat said.

One senior Senate aide said that effectively delays action until after the next Senate recess in two weeks.

But regardless of which piece Democrats bring up, Reid said Wednesday that they would all be paid for with the same tax increase on millionaires that Senate Republicans have rejected.

Senate Minority Leader Mitch McConnell said there are some actions that Congress could take to help the economy and create jobs, but he said they should be considered by the Joint Committee on Deficit Reduction.

“There are some pieces of what the president has recommended for which there is some Republican support, and as I indicated, I think the Joint Select Committee should look at some of those, and we anticipate they will look at some of those,” the Kentucky Republican said. 

McConnell declined to say which pieces he thought Republicans could support, although Sen. John McCain (R-Ariz.) said the payroll tax cut could be part of an agreement.

The idea that seems to have the broadest support among Democrats, meanwhile, is to move an infrastructure-only bill.

“My No. 1, my No. 2, my No. 3 is infrastructure,” Senate Budget Chairman Kent Conrad said.

But the North Dakota Democrat added that he would also vote for another temporary cut in the payroll tax, even if it wasn’t initially offset.

“The economy is very weak and needs a lift,” he said.

Sen. Joe Manchin (D-W.Va.), who voted to cut off debate on the president’s jobs package but said he would have voted against the bill itself without changes, said infrastructure should be the priority. Manchin said he doesn’t know of any Republicans or Democrats who don’t need more infrastructure in their states and suggested paying for it with war savings by bringing troops home from Afghanistan.

Democratic aides, however, have suggested the payroll tax cut may be a better vehicle, pitting tax cuts for workers and small businesses against millionaires.

Sen. Carl Levin (Mich.) urged his fellow Democrats not to break up the bill but instead force an old-fashioned filibuster and take the issue to the public with the bully pulpit.

“We should keep the bill together,” he said.

Sen. Joe Lieberman (I-Conn.) also showed little enthusiasm for backing a smaller package.

“I’m very skeptical about most of it,” he said, “even the payroll tax cut. … I’m not convinced there’s been evidence to show that produces enough jobs.”

But even Lieberman said one idea appeals to him — setting up an infrastructure bank.

Lieberman, like McConnell, said the best plan is to submit ideas to the super committee and hope it can hash out a bipartisan agreement.