"formidable pressure" is correct and usable in written English.
You could use it to describe a situation in which there is an overwhelming amount of pressure, usually due to external factors. For example, "The deadline for this project was fast approaching, combined with formidable pressure from our manager, made the task seem almost impossible."
Compared with these other formidable pressure groups, consumer protection is the poor relation of the lobbying family.
Dr. Holloman found himself under formidable pressure to close and curtail services, the last thing he wanted to do.
But watching Billy buck the formidable pressure of his family to pursue ballet was hard to resist, and Ethan was clearly struck by the accomplished pirouettes of David Alvarez, who played the title role at ourperformance.
Then, the long-delayed but crucial issues of Jerusalem and refugees, Israel-Palestine borders and Jewish settlements, were finally addressed, with formidable pressure on Yasser Arafat to concede the match and yield any further claims against Israel, a pressure he successfully resisted with the reward of Arab accolade and American-Israeli contumely.
Together, they bring formidable pressure for participants at the upcoming U.N. Paris Climate Summit to reach agreement for aggressive actions on behalf of present and future generations.
Under formidable international pressure to pull back from the West Bank, Prime Minister Sharon has been reinforced in his defiance by a series of Palestinian suicide bombings that have come at crucial moments.
More recently, I bowed to formidable family pressure to get our dog Tatty, mostly because she looks like a black version of Snowy and so I thought she might lead us to adventures.
The young tenor overcame formidable obstacles the inevitable pressure of a Met début, the added pressure of replacing a legend, the Antarctic ice-floe tempos of James Levine to make a powerful impression.
Two Chinese companies in particular, Xiaomi and Huawei, have emerged as formidable rivals, putting pressure on Samsung in China and India.
The young tenor overcame formidable obstacles — the inevitable pressure of a Met début, the added pressure of replacing a legend, the Antarctic ice-floe tempos of James Levine — to make a powerful impression.
He gave a plug to Hillary on ABC News last night, calling her a "formidable candidate," even under pressure, who "understands the klieg lights".
