House Republicans might bring a proposed constitutional amendment to balance the budget to the floor as early as the week of Nov. 14 — even as the chamber is embroiled in yet another short-term spending battle.

According to an email circulated to House offices Tuesday by the Balanced Budget Amendment Caucus and an aide to its chairman, Rep. Mike Coffman (R-Colo.), “This is not public information yet, but I wanted to make sure that caucus Members know that the vote for the Balanced Budget Amendment … is likely to be the week of November 14th. That is also the week a new [continuing resolution] will have to be passed, barring any unexpected flurry of action in the Senate.”

However, the email notes that “as of now, there is no agreement as to what version of the Amendment will be voted on, but Leadership and others are working on that question.”

The version the chamber considers could dramatically affect its fate in the House and Senate. Republicans have been pushing for a version that would essentially force the president to balance the budget without using tax increases.

Although a handful of Democrats could end up backing that measure, it would not see the kind of broad support a different version of the amendment has received in past years that would entail spending cuts and tax increases.

Both chambers are required to vote on a balanced budget amendment this fall under the terms of this summer’s debt deal.

A spokeswoman for House Majority Leader Eric Cantor (Va.) — who sets the floor schedule — declined to comment for this story. However, Cantor has previously said he would not support bringing another continuing resolution to the floor, preferring for the House and Senate to come to some sort of an arrangement on fiscal 2012 funding.

But the Senate is still slowly working its way through appropriations bills, and barring a deal to move either an omnibus or a series of minibuses over the next two weeks, a CR has become an increasingly likely possibility.

Jonathan Strong contributed to this report.