The phrase "a much higher hurdle" is correct and usable in written English.
It can be used to describe a significantly greater challenge or obstacle that must be overcome.
Example: "The new regulations present a much higher hurdle for small businesses trying to comply with the law."
Alternatives: "a significantly greater obstacle" or "a far more challenging barrier."
It has a much higher hurdle to cross".
This is what's really at stake, and it creates a much higher hurdle for approval.
But that's a much higher hurdle than the already formidable barriers in place to discourage lawsuits against the government.
For many smokers, emotional dependence on smoking is a much higher hurdle to overcome than their chemical dependence.
That provision says bills backed by the Beijing-selected chief executive of Hong Kong need only a simple majority to pass, while bills and amendments introduced by members of the legislature must clear a much higher hurdle: the support of a majority of the democratically elected members plus a majority of the members representing functional constituencies.
This combination of the implantation and waiting two weeks after surgery before treatment with the inhibitor provides a much higher hurdle to assess drug efficacy.
But that would be a much higher political hurdle for the Super Committee to jump over.
A few months ago he told me that the Thames Estuary scheme had much higher hurdles to jump over than its competitors at Heathrow and Gatwick.
Much higher hurdles remain to be crossed before the President is likely to visit the Soviet Union.
In the past, it has been disappointing to see an entire sports team appointed MBE for transient success when those who have, unremunerated, given years of service have much higher hurdles to leap before they can hope [for] an award".
When he woke up this morning, he said his knee looked irritated and red, but he has overcome much higher hurdles than that in his career, which has seen him rise to fame from an impoverished background.
