The way I see it Layton wanted to become President, or have a position equivalent to President and higher, and more forcibly direct the Federation High Council. If Sisko had not thwarted Layton's plans then I guess Starfleet and the High Council would have believed that a Dominion invasion is imminent. Layton would enforce martial law and probably conduct false flag terror operations to scare the races of the Federation into believing the Dominion was an immediate threat ready to wipe out the Federation if it was not prepared.
Layton would probably create a police state under the fašade of a democratic decision and then he would not stop because he would need more and more control to keep his plans alive. Layton would become a dictator, the Federation would become more militarized, just like the Romulans and Cardassians. Ironically the Federation -- under this new system -- would probably offer to help the Klingons conquer the Cardassian Union. All of it under the guise of protecting the Alpha Quadrant from the Dominion. The Khitomer Accords would be refreshed as the Federation and Klingon goals became the same.
Ironically though the Federation would never close the Bajoran wormhole, because then Layton would have to abolish these emergency security measures. But he wouldn't because you once acquire power through corrupt means you tend to cling onto it lest ones true intentions are publicly revealed.
Let's not forget Section 31, I'm pretty certain they would not let Layton get away with a take over of the Federation. Because Section 31 are a smart bunch and they would know that this would lead to civil war.
If anything Layton should have made his move in conjunction with Section 31 after the Dominion war, because I'm certain Section 31 would desire stronger measures in their desire to protect the Federation from its enemies. Plus at a time when Federation races are reeling over the terrible death and destruction the Dominion wrought, that's when Layton should have carried out his coup; all under the guise of protecting the people of course.