“Where wages are not regulated by law, all that we can pretend to determine is what are the most usual; and experience seems to show that law can never regulate them properly, though it has often pretended to do so.” 
― Adam Smith, The Wealth of Nations

Under the Service Contract Act ("SCA"), the wage payment "will be satisfied by the timely payment of such wages."  29 C.F.R. 4.167.  What constitutes timely payment is mostly left up to State law, provided payment is at least semi-monthly.  

Under the Copeland Anti-Kickback Act, construction workers on Davis-Bacon Act (“DBA”) covered projects, must be paid by a weekly certified payroll. 20 C.F.R. 3.3. This is the origin of the weekly payroll requirement for US Government construction projects, which has been in place since the 1930’s. And many states have their own prevailing wage or little DBA laws of their own that also require weekly payroll on state government contraction projects. It is this statutory difference that causes the variation in payroll frequency between service and construction work for the Government. Unlike the Copeland Anti-Kickback Act, which covers most US Government construction projects, the SCA does not dictate the weekly payment of wages.  So while DBA covered construction workers' wages must be paid weekly, other federal law does not necessarily require such frequency of payment.  

Under federal service law, with respect to covered employees, the employer may set a pay period of any duration it likes under the SCA so long as it "is no longer than semi-monthly."  See 29 C.F.R. 4.6(h).  In addition, the SCA rules provide:  

(b) The Act does not prescribe the length of the pay period. However, for purposes of administration of the Act, and to conform with practices required under other statutes that may be applicable to the employment, wages and hours worked must be calculated on the basis of a fixed and regularly recurring workweek of seven consecutive 24-hour workday periods, and the records must be kept on this basis. It is appropriate to use this workweek for the pay period. A bi-weekly or semimonthly pay period may, however, be used if advance notification is given to the affected employees. A pay period longer than semimonthly is not recognized as appropriate for service employees and wage payments at greater intervals will not be considered as constituting proper payments in compliance with the Act.

29 C.F.R. 4.165(b).  

The so-called Contractor Minimum Wage Executive Order, if and when it is ever added to your contracts, also specifies that at least minimum wage an hour be paid by a semi-monthly payroll or more frequently.  (As of January 1, 2019, the E.O. 13658 minimum wage will be $10.60 per hour. See 83 FR 44906 ).

In addition, as noted above, of course, covered employers must comply with relevant state laws, if applicable.  Most states have a frequency of payment law and/or a last paycheck law, except perhaps Texas.  Some states have weekly payroll requirements in certain circumstances. E.g., Rhode Island (although it can be waived by the State).  Also, some employees work on an exclusively state funded contract with its own state prevailing wage that may also impose a weekly payroll requirement.  An example of a general frequency of wage payment state law requirement is the Virginia Payment of Wage law, which provides as follows: 

All employers operating a business shall establish regular pay periods and rates of pay for employees except executive personnel.  All such employers shall pay salaried employees at least once each month and employees paid on an hourly rate at least once every two weeks or twice in each month [with some exceptions].  

Code of Virginia § 40.1-29.  So Virginia allows semi-monthly payment too. Obviously, before an employer sets its payroll frequency, it needs to confirm the particular state law requirements where it has operations, and adjust its practices to confirm to the strictest state law, and review its contracts, or run different payroll frequencies in each state with a stricter requirement.