They've already signed on, as has AMD. They were a bit concerned about the signing issue, but feel confident that as long as they control the hardware (and thus the "top-level" authority), that it won't be a problem for them.
Dell already ships Red Hat Linux as an option. So do others. If Microsoft does get Intel to go with a secure BIOS line, Intel will still sell chips with a different BIOS to enable other OS'es
If the laws currently being proposed are allowed to pass (and they have a lot of support), Intel won't have an option to offer an alternative, because only "secure" (i.e., those that incorporate so-called digital rights management) operating systems will be legal. Linux could get approval by submitting itself to the signing authority, but it would no longer be the "free" model (i.e., build whatever / whenever you want) any longer.
Because if they don't other chip makers will fill the need.
AMD has already signed on as well, so the only alternative would be Via (whose x86 core is a full generation behind the competition). And if the legislation passes, it would be illegal to import them in any case. Of course, Intel could just sign a copy of Linux (Red Hat or some other distribution), but that won't really solve the fundamental problem, because Intel won't do so unless that particular build incorporates DRM / similar technologies. When systems like this are fully implemented, the days of having full control of your computer are over. You won't even be able to write code from scratch, since it will never run unless you have signing authority, which the corporations can't give out (even assuming they wanted to do so) without breaking the proposed laws.