There's two options here
There are two options here
I hear a lot of people say the first line (or something similar), but isn't that incorrect? Isn't it plural and therefore you should use "there are"?
Here's an edited version of a post I did for ELU on a similar question (which got closed):
The existential construction takes there as a subject. There has no meaning, and often the verb takes its agreement from the complement of the verb BE. So if the Noun Phrase after BE is plural, the verb will usually be in a plural form. If the Noun Phrase is singular it will usually be singular:
Notice, however, that in the examples above, the subject and the verb BE are not contracted. In normal speech these will nearly always be contracted. We will use there's instead of there is. It is also quite common nowadays to see them contracted in writing, normally in informal texts, although you can find instances in prestigious newspapers like the Times, for example.
Now when the subject there and BE are contracted like this, the verb doesn't need to agree in any way with the following Noun Phrase. Therefore with regard to the Original Poster's example, if they had said:
*There is two options here.
... this sentence would be regarded as ungrammatical by most, if not all speakers. However because they did contract there and BE, it is grammatical:
There's two options here.
This makes this sentence similar to a famous lyric from one of John Lennon's songs:
Imagine there's no countries.
Or usages such as:
There's times when I've wanted to box his ears
Having said this, despite the fact that this is a well documented aspect of the grammar, some prescriptivists are bound to take offense at this. They will insist that it's ungrammatical to use a plural noun after there's. This will be despite the fact that they quite subconsciously actually use plural nouns after there's themselves quite frequently. They will appear about five minutes after I post this answer. They do make life fun though!
There are some other special situations where we might use there is with a plural noun phrase, even though it is not contracted. For example How many people live in your house? Well, there is me, my grandad, my mum and my aunt. If you'd like to read about these exceptions, there's some good posts here!.
I remember this one from English classes in school many years ago.
It was explained to me by my English teacher as follows:
As several people already mentioned are is the grammatically correct word to use.
The reason that in colloquial speech is is often used in such a phrase has mainly to do with the fact that the speaker is dealing with 2 concepts (one plural and once singular) at the same time.
Example: "There's 2 answers to the question"
"Answers" is obviously plural, but there is one question. The speaker ties the verb to "question" and is inclined to use is.
This even happens if "to the question" isn't really spoken. The speaker is still thinking about it.
Another example: Where's the cattle?
The speaker probably has a place (singular) in mind, which (unconsciously) affects his/her use of the verb.
Yes, "There's two ..." is incorrect. The subject and verb should agree in number.
And yes, in informal speech you will hear people say this. But that doesn't make it correct. People say lots of grammatically incorrect things in informal speech, because when you're talking, you don't necessarily have the sentence planned out when you start, or you're just not paying careful attention to your word choice.