Of course, the Saudi government is going to get involved if Saudi women are speaking out against their roles in society. If these women are speaking publicly, it would be even worse, so social media is absolutely going to grab the attention of the government. They know these women can reach a lot of people and that their cause could attract some attention.
The Saudi Arabian government will likely crack down on women launching a Twitter campaign demanding an end to male guardianship. Male guardianship has been a part of Saudi culture forever. These women are putting themselves at risk by speaking out against the policy. The government is likely to arrest and imprison them.
Once someone realizes their own freedom there is really no way to stop their progress. The women of Saudi Arabia have more than likely been educated abroad and have seen open societies. They want to bring that to their own homeland and will force the issue which has begun with the guardianship problem. The government will show some resistance but it will be futile.
The Saudi Arabian government will not crack down on the women that launched the Twitter campaign demanding an end to male guardianship. . Technology is a great equalizer, with many able to see the outside world and express themselves. This spreads the word to the entire world, and places pressure on the monarchy to change.