MOSCOW — “Time to shove off” is the name of a Web site for people who are fed up with life in Russia, and it is becoming a catchphrase for those dismayed by the newly announced plans of Vladimir V. Putin to keep a grip on power for perhaps two more terms as president.

“A year ago I told all my friends who were leaving that I would never do that, no way!” wrote a magazine editor named Yevgeniya Lobacheva in a posting on another Web site. “But I have only one life. Twelve years! I will be 43!”

Mr. Putin has already been in power for 12 years — the first eight as president, the past four as a prime minister with de facto executive power. Now, the prospect of what many Russians are already calling a “period of stagnation” has set off a new wave of declarations of nonallegiance to a nation where corruption and an inflexible top-down system are squeezing off options for change and personal advancement.

“I want to live in a country where I don’t need to break the rules to live in comfort,” said Stepan Chizhov, 29, who markets board games like Monopoly and is preparing to leave for Canada with his wife next summer.