Majority Leader Harry Reid (D-Nev.) said Tuesday that the Senate will pass the House version of the war supplemental bill, most likely addressing the other programs that many lawmakers advocated for in a second economic stimulus package.

Speaking to reporters after the weekly Democratic luncheon, Reid said the Senate will “come back at a later time and do” the other projects that deal with disaster relief, children’s health care and the energy-assistance program.

Reid said Congress would address those programs in a second stimulus that would be voted on first by the House, when lawmakers return from the July Fourth recess.

“We hope to take that up next work period when we get back. It’s easier for [Speaker Nancy Pelosi (D-Calif.)] to bring something up than me … It’d sure be nice if they could bring something up quickly. I hope so, and we’ll follow through as rapidly as we can,” Reid said.

It is unclear if either the White House or GOP leaders would welcome a second stimulus package, as Republicans have argued that time needed to pass before lawmakers sought additional measures.

Reid’s desire for a second stimulus recognizes the extensive negotiations that took place between the House and the White House to arrive at a compromise bill to fund the wars in Iraq and Afghanistan that the president would sign.

The Majority Leader’s comments come one week after the House overwhelmingly supported the war spending bill that includes unemployment insurance, GI benefits and flood relief for the Midwest, which has been ravaged by heavy rain.

Among the things Senators will now have to forgo, for now, is an increase in the already $5.8 billion for levee repair in Louisiana, lobbied for by Sen. Mary Landrieu (D-La.), who sits on the powerful Appropriations Committee.

The Senate earlier approved a supplemental with $10 billion in additional spending over the House measure.