Are we heading for constitutional crisis as Sturgeon threatens to 'veto' Brexit

We can see in the headlines that Nicola Sturgeon is threatening to 'veto' Brexit on the grounds that consent from the Scottish Parliament is required to stop Scotland being subject to EU laws. See http://www.bbc.co.uk/news/uk-scotland-scotland-politics-36633244 Are we heading for a full blown constitutional crisis with Scotland simply refusing to withdraw from the EU?

Well, probably not in that sense, but the upshot is likely to be in a sort of quid-pro-quo that the Scottish Government's desire for a another independence referendum will be granted before the UK leaves the EU.
As is argued in a legalistic explanation which you can see at: https://waitingfortax.com/2016/06/25/can-the-scottish-parliament-block-brexit/ (and thanks to Paul Cairney for pointing this commentary out), it is the case that for 'normal' legislation the consent of the Scottish Parliament would be needed if Westminster wishes to amend the 1998 Scotland Act. And this Scotland Act specifies that Scotland is subject to EU law.

The apparent downside for the First Minister's strategy is that Brexit is hardly 'normal'! In practice Westminster could amend the 1998 Scotland Act and assume, with some confidence, that the judiciary would uphold Westminster's version of the law. Despite what some of the more excited supporters of Scottish independence may be tempted to suggest, the Scottish Government is not going to make a unilateral declaration of independence under these circumstances.

But then I strongly suspect Nicola Sturgeon realises the likely legal outcomes but is highlighting this issue as part of the pursuit of a strategy to induce the Westminster Government to grant a further 'indyref'. Failure by Westminster to give this concession, and an attempt to disarm the SNP Government by staging, and winning, a new referendum on Scottish independence, is likely to have increasingly problemmatic political consequences. Indeed as tempers rose in the years leading up to the 'Brexit' legislation being passed by Westminster the stage could be set for mass demonstrations, especially one timed for the day that Westminster passed the amendment of the 1998 Scotland Act. Thousands of demonstrating Scots arriving at Westminster..........etc etc

No, the most likely outcome is that Westminster will agree to another indyref to take the sting out of this. The problem for the Westminster Government in dealing with this is that now the ranks of nationalist voters are being supplemented by former unionists who are changing their tune after  their votes to remain in the EU have been frustrated. And there are some quite surprising shifts taking place.
For the moment the Scottish Government's storyline is to keep Scotland in the EU, as well as preparing the way for another referendum on independence. In this they will have the support of the Scottish Greens, giving the strategy a majority in the Scottish Parliament. Even the Scottish Liberal Democrats appear to be showing some sympathy with this and Kezia Dugdale is sounding pretty ambivalent.

Whatever people may say, however, Scotland can't stay part of the EU and part of the UK if the UK leaves the EU. Apart from anything else, the EU will not entertain an application from just a part of another country. Scotland will have to leave the UK first, and then apply to join the EU. But in that case the EU is likely to be a lot more helpful to Scotland than they were in 2014. Many in the EU would want to reward Scotland. Meanwhile many in the EU want to punish  the UK with poor trade terms in order to stop other countries (eg the Swiss) picking and choosing rights such as immigration controls.
The Institute for Fiscal Studies  say there would be big economic penalties for Scotland in leaving the UK. Certainly public finances may suffer very substantially as long as oil prices stay relatively low. But in the current uncertain economic circumstances facing the UK (or reduced UK), such arguments may not carry as much weight as you would think, especially with bravado from Holyrood being spread about possibilities for Edinburgh replacing London as an EU financial centre etc. Besides, how seriously did the people who voted to leave the UK in our recent EU referendum take the predictions of economic disaster? Identity politics seem to be ruling the roost in today's world, like it or not.

Of course it is possible that this strategy could be undermined if Marine Le Pen won the French Presidency next year and talked about 'Frexit'. But it doesn't look like she'll win at the moment. It is beginning to look like it will be a struggle for a divided 'rest of UK' and a weakened unionist position within Scotland to hold the unionist line in another indyref which is may occur as early as a year or 18 months time. Yes, the break-up of the UK is looking now like a very plausible proposition. In that way then, we are heading for constitutional crisis.