Reid refused an offer to take the cloture vote early, then said the GOP was the one invoking "filibuster" (which is generally speaking, delay). The cloture vote on what is sitting in the senate will happen on schedule.
The house and senate are independent bodies, and while the chances of both writing the same bill is essentially zero, what is going on is that Boehner will bring up a house bill, written to contain the same thing that Reid is proposing in the Senate. The house vote is purely symbolic, assuming it is defeated.
-- The Senate and the POTUS are officially irrelevant. --
Under the constitution, all have a role in making law.
Mind you, I think the federal government is worse than worthless. It is a parasite. It will eventually kill its host, and then it too will die. Can't happen fast enough to suit me.
Senate Republicans want a 60-vote threshold for a debt-limit bill to pass the chamber, but it’s actually Democrats who are enforcing the filibuster on their own legislation, insisting on delaying a vote until 1 a.m. Sunday morning.
In lieu of a Senate vote, House Republicans themselves will introduce and then vote to kill the Reid plan on Saturday afternoon as a way to try to force negotiations into the next phase.