plawolf
Lieutenant General
A "limited scale military operation" inherently carries the risk of escalating to a broader conflict. Both parties get a vote on such matters. And if there is undoubtedly "huge pressure" on the Chinese government to act, why would one expect the pressure on the Indian government to be any less, such that they would accept a limited defeat without further escalation?
Essentially, the gamble in such a situation is that India's institutions, and the decision-makers involved, are far-sighted enough to accept a limited defeat (or find a way to de-escalate before that point), acting in the national interest rather than out of concern for one's career, the image of one's party, etc. Who here has that much confidence in the Indian government?
Because the stretch of boarder in question is pretty much the only part of the boarder where India enjoys terrain advantage, which is why India chose it to start this stand-off.
China enjoys absolute escalation advantage in every conceivable escalation scenario. The more the Indians escalate, the greater China's military advantage becomes, and the bigger the loss for India.
China will try to eject the Indian troops in such a way as to not spill blood, and to allow the Indian government some maneuvering room to climb down without loosing too much face.
However, if the Indian government is too stupid and/or stubborn to accept the favour, China will make a point of teaching India's leaders the error of their ways in no uncertain terms, least they forget themselves and make a similar mistake in the future.
If India pushes China that far, do not think Sikkim and Bhutan liberation and independence would be off the table. After all, the treaty India trampled and effectively ripped up by crossing that stretch of settled boarder is also the foundation for Chinese acceptance of Indian annexation of Sikkim.
It is either through great good fortune or judgement that India's timing was very good since China is mainly concerned with Korea and internal politics and do not want a war. Because the scale of the loss China could easily inflict on India is truly eye watering if China wanted to pick a fight with India.