Hitesh,
You will most likely hear "there is" in a lot of cases, even when the noun and the verb do not agree. This has more to do with the relative ease of pronouncing the contracted form of "there is" versus "there are".
You can try this yourself. Say "there's" without adding any syllables. Notice how easy it is. It doesn't elongate the word at all.
Now try saying "there're" without adding or elongating any syllables. It's not so easy (especially if your accent is
rhotic). As a result, English speakers tend to prefer "there's" when speaking quickly and informally, resulting in many grammatical errors.
To sum up, it is not grammatically correct to say "there's [there is] too many things to do"; however, as long as you can confidently contract "there's" in one, non-elongated syllable, most native English speakers won't even notice the error.
EDIT: not that I'm suggesting you should get in the habit of making grammatical errors!