The White House on Monday issued a broad veto threat against a pending House appropriations bill funding the Department of Homeland Security, declaring the president would reject any individual spending bill not approved within a larger budget framework.

It’s a more targeted shot across the bow from President Barack Obama, who has insisted he will no longer negotiate around extending the nation’s borrowing capacity. The government is projected to hit its debt limit early this fall — or roughly the same time as this fiscal year’s appropriations bills are set to expire. The current spending levels were set by 2011’s Budget Control Act, the legislative result of the last major fight on the debt limit, when Republicans exacted an austerity policy from Democrats in exchange for raising the debt ceiling.

From the administration’s statement of policy:

“Prior to consideration of appropriations bills the Congress should complete an appropriate framework for all the appropriations bills. More than a month has passed since the deadline for action and the Congress has yet to appoint conferees and agree on a budget resolution.

“Unless this bill passes the Congress in the context of an overall budget framework that supports our recovery and enables sufficient investments in education, infrastructure, innovation and national security for our economy to compete in the future, the President’s senior advisors would recommend that he veto H.R. 2217 and any other legislation that implements the House Republican Budget framework.”

In January, the GOP suspended its demand for cuts in exchange for a debt limit extension because Republicans said they believed they could maximize their position for more cuts on a delayed timeline. To be sure, Obama had previously said he wouldn’t negotiate around the debt ceiling only to later back down and do so. On the other hand, Senate Democrats also want to give new Appropriations Chairwoman Barbara A. Mikulski of Maryland room to negotiate a larger appropriations agreement with her GOP counterpart, Richard C. Shelby of Alabama.

Of course, even if leaders say they are deferring to Mikulski, tying the debt limit to a larger spending blueprint would likely hamstring Senate appropriators. The last time Congress approved any appropriations bills outside of a continuing resolution was for fiscal 2012, when they approved a handful of so-called mini-buses in addition to a larger continuing resolution that bundled the majority of spending provisions.

The Military Construction-Veterans Affairs spending bill is typically non-controversial enough that both chambers can approve it outside a larger spending framework. Threatening to veto individual and less controversial spending bills complicates Mikulski’s negotiations, but sends a clear signal that Obama is looking to solve problems caused by the automatic across-the-board spending cuts known as sequestration.