House Republicans may have lost their battle against Planned Parenthood in the compromise with Democrats on a spending bill agreed to last Friday, but they will continue to fight the war.

On Tuesday, the House majority leader, Eric Cantor, said Republicans would continue to try to strip Planned Parenthood of all of its federal funding, and suggested that the matter could be used as a bargaining chip in debate over a budget for the 2012 fiscal year and the question of whether to lift the federal debt ceiling.

When asked if the matter could come up in those negotiations, he said, “Where I think that we have consistently been, is to reflect that we believe very strongly that government dollars should not be used to fund abortion.’ (In fact it is already against federal law to use federal dollars to obtain an abortion.)

House Republicans sought to take all federal dollars that go to Planned Parenthood and other family-planning groups to help poor women and turn them over to the states instead. This was a nonstarter for President Obama and Senate Democrats and so this policy rider, which threatened to derail the entire plan to avert a government shutdown, was removed.

Instead, both the House and Senate are scheduled to vote Thursday on a stand-alone bill to take away all federal funds from Planned Parenthood, a measure that was part of a House spending bill passed in February that failed in the Senate. The current bill will likely face a similar fate in both chambers.

The spending bill agreed upon Friday also cuts federal dollars used for family-planning services under the Title X of the Public Health Service Act to $300 million, from $317 million.

Although Democrats and Republicans are fighting largely over how to tame the federal deficit and lead the nation out of a protracted fiscal crisis, it seems increasingly clear that the two sides are also going to be at loggerheads over the profound social issues that have divided the nation for the past several decades.