However, this has almost happened before, so don't get your hopes up.
Pakistan came close to being named a state sponsor of terrorism in 1992 when then Secretary of State James Baker charged then prime minister Nawaz Sharif of supporting terrorism in Jammu and Kashmir. The then US envoy in Islamabad Nicholas Platt conveyed to Sharif that "we (US) are very confident of our information that your intelligence service, the Inter-Services Intelligence Directorate, and elements of the Army are supporting Kashmiri and Sikh militants who carry out acts of terrorism... This support takes the form of providing weapons, training and assistance in infiltration ... We're talking about direct, covert support from the Government of Pakistan."
In his talking points, Platt continued: "Our information is certain. It does not come from the Indian Government. Please consider the serious consequences to our relationship if this support continues... If the situation persists, the Secretary of State may find himself required by law to place Pakistan in the U.S.G. [United States Government] State sponsors of terrorism list... You must take concrete steps to curtail assistance to militants and not allow their training camps to operate in Pakistan or Azad Kashmir."
The situation was defused by Sharif government removing then D-G of ISI Javed Nasir even as Washington was going through a transition phase (from Bush Sr to Clinton).