"Until Reid guarantees a 60-vote threshold on all amendments, a vote for cloture is a vote for Obamacare," Cruz wrote, calling for a public groundswell to motivate legislators from both parties to back his approach.
He showed the raw politics of his strategy by targeting Democratic senators who face re-election next year in conservative-leaning states.
"If you're a Mark Pryor, if you're a Mary Landrieu, running for re-election in Arkansas and Louisiana, and you start to get 5,000, 10,000, 20,000, 50,000 calls from your constituents, suddenly, it changes the calculus entirely," Cruz told "Fox News Sunday."
However, opposition to Cruz's approach by senior Senate Republicans including McConnell, McCain, Tom Coburn of Oklahoma, Bob Corker of Tennessee and others show it lacks the votes for a successful filibuster.
Critics warn that bombastic political rhetoric and promises that can't be fulfilled can undermine serious efforts to move forward.
"I think one of the things we are struggling with is establishing what's a realistic expectation for what we can accomplish when we control one out of three parts of the elected government," GOP Sen. Pat Toomey of Pennsylvania told MSNBC on Monday. "When you control only one out of the three, you don't get to dictate all the terms. But you can have some wins if you're smart and if you focus on where that opportunity lies."
Democratic Sen. Chuck Schumer of New York said the end result would be worked out amid all the political maneuvering.
"There are obviously going to be negotiations going on while this is happening," Schumer told MSNBC on Monday. "So everyone's going to know what's happening. Everyone's going to know the inevitable outcome."
Despite all the procedural hoopla, Reid and Democrats intend to cut out the provision that defunds Obamacare and return the spending plan to the House.
That would put the pressure on Boehner.
He could decide to set aside the measure, essentially declaring a stalemate between the House and Senate that would bring a government shutdown, which he has said he opposes.
Boehner also could bring the revised spending plan up for a vote and possibly allow for new amendments.
This is where things get tricky.
Because the Senate procedural battles are expected to last all week, the House will be under pressure to act quickly to avoid a government shutdown beginning October 1.
Boehner could allow a vote on the "clean" resolution sent back by the Senate, which would likely pass with support from all the House Democrats and a few dozen Republicans to reach the 218 majority threshold.
However, most House Republicans would vote "no" in that scenario, further weakening Boehner's already shaky leadership of his party's caucus after a similar result in a past budget battle.
Boehner also could allow GOP amendments to be added, such as a proposal to delay implementation of Obamacare for a year.
The intent would be put the pressure back on the Senate, and particularly Senate Democrats, to reject the revised House proposal and therefore risk getting blamed for a government shutdown.
That might not happen until after October 1 with a shutdown already begun, leaving Republicans vulnerable to the public perception they were responsible.
Recent polling shows growing public opposition to Obamacare, but much greater dislike for a government shutdown, particularly among independent voters considered crucial to presidential hopefuls. In addition, more respondents indicated they would blame Republicans for a shutdown.
The deadline to increase the federal debt ceiling -- how much money the government can borrow to pay its bills -- is coming up in mid-October, presenting another opportunity for Cruz and other Republicans to go after Obamacare.
House Republican leader Eric Cantor of Virginia already has said the House will consider a debt ceiling measure this week with a wish list of GOP priorities attached, including delaying Obamacare for a year and launching construction of the Keystone oil pipeline from Canada.