Sheremetev descended from the same old Moscow milieu as the Romanovs; he was their relative and supporter.
Sheremetev took an active part in the Zemsky Sobor of 1613; he's ascribed famous words (in a letter to prince Golitsyn, perhaps apocryphal): "Let's elect Misha Romanov, he is young and stupid, he will be obedient to us".
In 1634 he was a head of Russian delegation (together with Alexey Lvov) in Russo-Polish negotiations and signed the Treaty of Polyanovka.
After Ivan Cherkassky's death in 1642 Sheremetev was appointed head of Russian government, but his power was feeble: court marshal Alexey Lvov had more influence, and Sheremetev was disliked by Prikaz dyaks.
His weak position was reflected in a contemporary chronicler's remark: "This Fedor was evil-tempered and unskillful in affairs".