That's according to lawmakers briefed by the White House chief of staff on Thursday.
The longest-serving member of Congress is set to retire after this year.
But immigration changes or Islamic State strikes could upend their best-laid plans.
The measure is expected to be quickly approved by the Senate, capping months of talks about revamping the VA health system.
Several big issues -- veterans' health care, highway construction funding and how to deal with the U.S.-Mexico border -- remain unresolved with just hours to go until recess.
A look at how momentum for the issue built, then fell fast.
The process, resembling the secrecy of a papal election and the elimination rules of a televised singing contest, could take hours.
Meeting will come as White House weighs potential military options to address deteriorating crisis.
There's the speaker, the leader and the whip. What does each of them do? (And where did they come up with whip?!)
Four lawmakers -- two Republicans and two Democrats -- team up on the resolution. Support for the measure is unclear.