There is no quick answer to this question. It will depend on what type of blow you are talking about, and the answer will vary greatly depending on where you are arrested and the specific police officer who arrests you. The legal limit in the state of Texas is 0.08. Even if you provide a breath sample that is under this limit you may still be arrested.
There are two different types of “blows” that are commonly seen in Texas DWIs. Sometimes an officer (often Texas State Troopers) will ask you to blow into a portable breathalyzer (PBT) on the side of the road. These are small hand-held devices that use fuel cell technology to estimate your blood alcohol concentration based on the amount of alcohol in your breath. In Texas courtrooms, PBTs cannot be used to show your exact level of alcohol concentration. However they can be used to show the presence of alcohol in your body. Even though the specific number the PBT spits out cannot be used as evidence at a DWI trial, the officer can and will use it to decide if whether or not you should be arrested.
The other “blow” is one that takes place at a police station with an Intoxilyzer. Intoxilyzer is a brand name. They are made by a company called CMI. The same machine is used throughout Texas, and these machines and maintained by the Texas Department of Public Safety. The Intoxilyzer is supposed to be more sensitive and more accurate than the PBTs, so the specific number generated by this machine can be used against you.
By the time you are asked to give a breath sample into this machine, you will already be arrested for DWI. Depending on where you are when you blow under, you may be released right away. However, in some places, like San Antonio, it is likely that the officer will ask a judge to sign a warrant to draw your blood. The arresting officer may believe you are intoxicated by drugs or a combination of drugs and alcohol. Ultimately, it is the decision of the officer whether or not to arrest for DWI, and it is the decision of the elected prosecuting attorney for the county to decide if they will formally file the charges and pursue the case against you.