A day after the Senate defeated President Obama’s $447 billion jobs bill, the question today on Capitol Hill is what’s next?

Both parties will huddle with their respective caucuses this afternoon in closed-door luncheons where discussing the next steps will be the top priority.

The first step will be breaking the jobs bill up into the pieces that can pass and working to move the individual parts toward bipartisan passage. It will be another painstaking adventure through the partisan divide on the Hill as lawmakers decide on what they can actually agree, especially at a time of particularly increased tensions.

Both parties say the piecemeal approach is now the new end game.

“Democrats care so much about creating jobs that we’ll give our Republican colleagues another opportunity to do the right thing,” Senate Majority Leader Harry Reid, D-Nev., said on the Senate floor this morning. “We’ll move forward in the best way that we can to put these matters before the American people if necessary, piece by piece.”

Senate Minority Leader Mitch McConnell, R-Ky., said this morning, ”I have some optimism that we’ll be able to come together on pieces of it that we think make sense.”

There is little agreement on the pieces so far, as both sides quickly regrouped after Tuesday night’s defeat.

One of the first pieces that might be plucked out of the jobs bill and moved toward passage individually is the 2 percent payroll tax cut through 2012.

Democrats will point out that most Republicans, including Minority Leader McConnell, have said that a payroll tax cut would put money back in the hands of businesses and individuals to help aid in the economic recovery.

Other pieces that might be pulled out of the jobs bill and passed individually are proposals for tax credits for businesses who hire out-of-work veterans, the extension of emergency unemployment benefits, infrastructure spending and making permanent the 3 percent withholding provision for government contractors.

McConnell pointed to one proposal, however, that’s going nowhere with his caucus: the Democratic-added provision of a 5.6 percent surtax on Americans earning more than $1 million.

“As far as I know, there’s not a single Republican who thinks it’s a good idea to raise taxes on over 300,000 business owners, which is what would happen under the so-called millionaires surtax,” he said. “So there are parts of it that we very much disagree with.”

Individual components of the jobs bill will be up for consideration in the next few weeks, the Democratic Senate leadership says.

The White House supports a piecemeal approach. After Tuesday night’s defeat of his bill, Obama said ”we will now work with Sen. Reid to make sure that the individual proposals in this jobs bill get a vote as soon as possible.”