House lawmakers will spend the week of June 2 debating the budget resolution and hashing out a way forward on the Senate’s version of the war supplemental bill, which includes $10 billion more in domestic spending than sought by House Democrats.

House Democrats left town for the Memorial Day recess having been victims of an unexpected ambush by their GOP counterparts that resulted in the defeat of $170 billion in emergency war funding. Unless the Pentagon draws money from other defense operations, the deadline for continuing funding for the war is June 15.

As part of the supplemental, the House did pass policy restrictions driven by fiercely anti-war Democrats and a domestic spending provision that included expansive GI benefits funded by a tax increase on the rich.

The Senate responded by approving an even bigger domestic spending provision, without the tax increase, rejecting the war policy changes but approving funding for operations in Iraq and Afghanistan.

A senior Democratic aide said House leaders are “still reviewing the Senate bill” and “looking to make changes to the domestic part.”

House Democratic leaders will meet early in the week to discuss how to proceed with domestic spending in the bill. Asked if House leaders are prepared to accept the two other Senate changes to the bill — the inclusion of war funding and the deletion of Iraq policy changes — the aide said, “I believe that is correct.”

Supplemental negotiations are focusing on the fact that “we would like [domestic spending items] to be similar to what the House originally passed.”

Also on tap for the week is the fiscal 2009 budget resolution, for which Democrats already passed a rule. House leaders are still working on timing with regard to this and the supplemental, said the aide.

Both measures are expected to come up late in the week. In the meantime, the House will wade through a mix of non-controversial bills, including two bills set for a Rules Committee hearing on Tuesday: a school construction bill and a bill to reauthorize funding for parks and historical sites around the Chesapeake Bay watershed.

After the chaos over the deletion of an entire section of the farm bill before the recess, a senior Democratic aide said the House does not plan to take up the remaining portion of the bill (known as Title III) this week.

The House voted the week before recess to override a veto of the farm bill by President Bush, but the version vetoed by the president mistakenly omitted an entire section.

There have been staff-level discussions about how to proceed with that bill, said the aide. Two options exist for advancing Title III language, and there are complications for both in the Senate, according to the aide. If lawmakers seek to advance a stand-alone Title III bill, Sen. Larry Craig (R-Idaho) may try to open it up for amendments. If lawmakers seek to pass the full farm bill again, Senate Republicans have hinted that they may object.

For now, said the aide, the House is going to wait to “let Senate Republicans figure out what they’re doing.”

Meanwhile, House Republicans will continue to focus their efforts on rising gas prices and their charge that Speaker Nancy Pelosi (D-Calif.) has failed to follow through on a promise to produce legislation to lower those costs, according to a GOP leadership aide.

“I expect that will be the focus of our procedural efforts throughout the month,” said the aide.

Beyond that, Republicans will redirect attention to the economy, starting the week after.

Asked whether to expect procedural fireworks from Republicans on the budget or the supplemental, the aide said GOP leaders will likely highlight that the budget includes “the largest tax increase in history” and that lawmakers “have already missed the deadline for passing a clean troop funding bill.”

Republican leaders will meet on Monday to develop their strategy for the week, said the source.