Can you travel to the US prior 1 months of tourist visa expiry?
I haven't heard or come across a rule which requires you have six months or more validity on a US visa to be allowed in. As the US Department of State website explains:
The visa validity is the length of time you are permitted to travel to a port-of-entry in the U.S.
Additionally, the visa expiration date shown on your visa does not reflect how long you are authorized to stay within the U.S. Entry and the length of authorized stay within the U.S. are determined by the Customs and Border Protection (CBP) Officer at the port-of-entry each time you travel.
What I believe you are talking about is the minimum validity of your passport that is required. From the London office website of US Embassy:
I understand that my passport needs to be valid for at least six months; is this correct?
The requirement that a passport is valid for travel for six months beyond the holder's stay in the United States is waived for certain nationalities. Please follow this link for further information.
Which means that if your country is listed among the ones in the PDF document, having less than six months validity of your passport will not be an issue. Additionally, other websites mention a minimum of 90 days validity is required for your passport (although this might be specific to if you're entering under the visa waiver programme) but the London office of US Embassy site states that is okay, and will only limit your stay period to whatever date your passport expires.
However, the New Delhi website of US Embassy implies you do need to get your passport renewed if it will be valid for less than six months from the time you enter.
Please obtain a new passport before your interview if:
Your passport is going to expire in less than 6 months after the time you enter the United States.
Your situation, then, will vary depending on what residency status you hold in a country as well as your citizenship.