After one week, the shutdown has already had dramatic effect on the economy, with some analysts estimating that it is costing approximately 300 million dollars per day so far.  Unfortunately, further negative consequences may result from the shutdown if a resolution is not reached soon.  The following government agencies and programs have been able to operate through the shutdown thus far, but may not be able to continue operations if the shutdown runs much longer:
Head Start:
Head Start officially closed on October 1, due to a lack of appropriations, but its programs operate based on grants that are distributed throughout the year.  The programs that were due to receive funding on October 1 were forced to shut down, which has thus far kept 5,000 children from receiving vital early educational services.  Unfortunately, more programs may run out of funding on November 1, depriving even more young children of these same educational services.  
Domestic Violence Programs:
The Office of Justice Programs disburses funds to rape crisis programs and domestic violence shelters across the country, but was unable to disburse any more funds after Friday, October 4.  Most of these types of programs and shelters are dependent on Office of Justice Program funding at least in part, so the shutdown will effectively withhold funding from programs aiding victims of rape and domestic violence from Monday, October 7, through the end of the shutdown. 
Food Programs:
The USDA Women, Infants, and Children program provides food to low income pregnant women, new mothers, and children.  The program currently has approximately 125 million in contingency funds to continue operation, but they believe that these funds may not last past October, at which point they will not be able to continue without a new appropriation.
Veterans Services:
Under current law, the Department of Veterans Affairs medical accounts are actually funded one year in advance.  Because of this, the VA will be able to pay for most of its medical programs through the shutdown.  Unfortunately, the same does not apply for its compensation and pension payments.  The Agency has informed Congress that if the shutdown lasts two to three weeks or more, it will run out of the resources it needs to make veteran’s benefit payments. 
Amtrak is managed by a separate, for-profit company, but still receives large funding from the US government.  Additionally, the shutdown reduces travel to the DC area, which further reduces income.  According to former board members and analysts, if the shutdown lasts more than a few weeks, there is a legitimate question as to whether Amtrak may need to alter operations, including cutting routes. 
United States Patent and Trademark Office:
The USPTO operates primarily as a fee based agency, and is currently running on reserve funds from last year.  It currently estimates it has enough reserve funds to operate for approximately 4 weeks, at which point it will reassess its funding and determine whether it can continue to run.
The Supreme Court:
The Supreme Court is still in operation, but it is only guaranteed to run through October 11, after the Court hears 6 cases.  After the 11th, the Court is unclear as to whether it will have enough funding to remain operational. 
As is obvious from the above list, if the shutdown is allowed to continue, important services that provide funds to children, victims of domestic violence, and our veterans will all cease to operate.  Find your Congressman here and let them know that you believe the government should reopen immediately to prevent these devastating consequences.