This is not that complicated if you think it through.
If Cruz and Lee do not muster 41 or more votes tomorrow against cloture Harry Reid gets to unilaterally add his amendment that funds Obamacare. Then, instead of having to win 60 (all the Dems plus some Reps) votes to pass his bill as would be the case if it were being voted on now, he only will need a simple majority to pass the bill funding Obamacare. That will provide political cover enabling all the Republicans (including to squishy establishment ones who don't really want to defund it) to vote "against" the bill funding Obamacare all the while knowing full well Reid and the Democrats will get what they want anyway because they are in the majority and will get to 51 votes just with Democrats. What Cruz wants to do is force the Republicans to actually vote "no" on the vote that matters; the vote to close debate (cloture) which will move the threshhold needed to fund Obamacare from 60 to only 51 out of 100.
This isn't actually a fight mainly against the Democrats... this is a fight against the establishment of the Republican Party.
But to continue... if somehow Cruz and Lee were able to get 41 or more Republicans to vote with them AGAINST cloture tomorrow... then Harry Reid would be faced the the dilemma of having to either hold no vote at all and take the blame for the shutdown... or to allow for a vote on the bill with the language defunding Obamacare which the Democrats would then vote against thus taking the blame (the Democrats) for the shutdown. Therefore, Harry Reid would then be in a position where these would be his two choices: defund Obamacare or vote for a government shutdown.
Most importantly, however, if Cruz and Lee were to get 41 votes tomorrow against Cloture, it would be a huge blow to the power and prestige of the worthless GOP leadership in the Senate as they would then have to actually do what they told their constituents they would (but many of them don't want to do because they are liars and statists); vote to defund Obamacare for real with no political escape clauses to absolve themselves of the blame for turning their backs on their constituents and their professed limited government principles. And any of them who did vote for Obamacare wouldn't survive the conservative backlash going forward for being traitors to the Republican voters (think McConnell in KY trying to fend off his tea party challenger after voting to fund Obamacare). To a certain extent this effort is about weakening and perhaps even purging the GOP of the worst of its establishment, statist-types.