The given compound, Me3CC(O)NMe2 (N, N-Dimethylpivalamide), contains several hydrogen atoms that can exhibit different chemical environments in the molecule. The number of singlet resonances observed in the 1H NMR spectrum of this compound at room temperature can be determined by analyzing the different types of hydrogen atoms present.

1. Identify the hydrogen atoms in the molecule:
In this compound, there are three types of hydrogen atoms:
- Methyl group (Me) attached to the carbon atom adjacent to the carbonyl group (C(O)).
- Methyl groups (Me) attached to the nitrogen atom (N).
- The hydrogen atom attached to the nitrogen atom (N).

2. Analyze the chemical environment of each hydrogen atom:
- Methyl group (Me) attached to the carbon atom adjacent to the carbonyl group (C(O)): These hydrogen atoms are in a different chemical environment and are expected to give a singlet resonance.
- Methyl groups (Me) attached to the nitrogen atom (N): These hydrogen atoms are also in a different chemical environment and are expected to give a singlet resonance.
- The hydrogen atom attached to the nitrogen atom (N): This hydrogen atom is in the same chemical environment as the other hydrogen atoms attached to the nitrogen atom and is expected to give a singlet resonance.

3. Count the number of singlet resonances:
Based on the analysis of the chemical environment of each hydrogen atom, there are three types of hydrogen atoms, each expected to give a singlet resonance. Therefore, the number of singlet resonances observed in the 1H NMR spectrum of Me3CC(O)NMe2 is three.

Thus, the correct answer is option A: 3.