なくちゃ (short forなくては), and なきゃ (short for なければ) are the most common colloquial abbreviations used to convey that something ‘must’, or ‘has to’ be done.
Like てはいけない (must not), なくてはいけない (must), and なくてはならない (must), these abbreviation forms can be followed by いけない, ならない, or だめ. However, they are usually omitted, without changing the meaning.
Structures like this are called 口語（こうご） (spoken/colloquial language) in Japanese. These casual variations can come across in a very similar way to words like ‘gotta’ in English.

• 今日（きょう）は家（いえ）の掃除（そうじ）をしなきゃだめだから、遊（あそ）ばない。
  Since I must tidy up the house today, I won’t hang out.
• 野菜（やさい）を食（た）べなくちゃいけない。
  I must eat vegetables.
• あっ、洗濯（せんたく）をしなきゃ。
  Oops, I gotta do laundry.
• 宿題（しゅくだい）をしなくちゃ。
  I gotta do my homework.

In these examples, a variety of forms have been used naturally. There is no ‘most natural’ form, and it will often depend on the speaker as to which they choose.
As with almost all grammatical structures, the shortest variations (not including いけない, etc.) are the most casual/used the most often.
There are several other ways that these common abbreviations can appear based on region, or even an individual speaker's preference. An example of this is なけりゃ, which is a (very) casual form of なければ.

• お前（まえ）がやらなけりゃだめだろ。
  You must do it! (Why aren't you doing what you must do?)

In this example, we can see that some of these less common variations are used specifically by certain genders (in general). なけりゃ itself tends to be used by male speakers, and may be considered a bit rougher than なきゃ, or なくちゃ, which can be used by anybody.