Find base resistance value
The \$\beta\$ value for a BJT applies to operation in forward active operation. In this circuit you want to operate the BJT in saturation. For saturation you should assume an \$I_c/I_b\$ ratio of maybe 1/10 of \$\beta\$. 

That will lead you to use a lower value for R1. You probably still won't get exactly 2 A of \$I_c\$. Rather, \$I_c\$ will depend more strongly on the power supply voltage and the effective resistance of the load.