The phrase 'pressing responsibility' is correct and usable in written English.
You can use it to refer to an urgent or important duty that must be completed soon and with great care. For example, "The mayor has a pressing responsibility to ensure the safety of all citizens during the storm."
If (as I suspect) he doesn't, doesn't he have an even more pressing responsibility to say he doesn't?
Mr. Klein started his job on Aug. 19, and his most pressing responsibility is ensuring a smooth opening to the school year.
Mosseri's most pressing responsibility will be reassuring users that the culture of Instagram and its app won't be assimilated into Facebook now that he's running things instead of the founders.
Here at home, the United States Congress has two pressing responsibilities: Pass the budget on time and pay our bills on time.
"With all these pressing responsibilities, one thing Congress should not be doing is sorting out the historical record of the Ottoman Empire," Mr. Bush said.
"With all these pressing responsibilities," Mr. Bush said, "one thing Congress should not be doing is sorting out the historical record of the Ottoman Empire".
One aide, who would discuss campaign personnel issues only on the condition of anonymity, said Mr. Gillespie was there not "instead of" Mr. Stevens but "in addition to" him, allowing him to focus more time on his most pressing responsibilities.
Given the housing crisis, HUD needs a strong leader who can live up to the pressing responsibilities of the agency and will put the issues ahead of political partisanship.
But risking personal funds can be trying, especially for those with families and other pressing responsibilities.
He continued making astronomical observations whenever he could, hampered by the poor position for observations in Frombork and his many pressing responsibilities as canon.
Most boards have robust processes for addressing their most pressing responsibilities, such as financial planning and compliance.
