This is the entire text of HR 3210 the Pay Our Military Act as found on the Thomas LOC website. Unfortunately the site seems to time out so you may need to repeat the search.

AN ACT
Making continuing appropriations for military pay in the event of a Government shutdown.

Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled,

SECTION 1. SHORT TITLE.

This Act may be cited as the `Pay Our Military Act’.

SEC. 2. CONTINUING APPROPRIATIONS FOR MEMBERS OF THE ARMED FORCES.

(a) In General- There are hereby appropriated for fiscal year 2014, out of any money in the Treasury not otherwise appropriated, for any period during which interim or full-year appropriations for fiscal year 2014 are not in effect–
(1) such sums as are necessary to provide pay and allowances to members of the Armed Forces (as defined in section 101(a)(4) of title 10, United States Code), including reserve components thereof, who perform active service during such period;
(2) such sums as are necessary to provide pay and allowances to the civilian personnel of the Department of Defense (and the Department of Homeland Security in the case of the Coast Guard) whom the Secretary concerned determines are providing support to members of the Armed Forces described in paragraph (1); and
(3) such sums as are necessary to provide pay and allowances to contractors of the Department of Defense (and the Department of Homeland Security in the case of the Coast Guard) whom the Secretary concerned determines are providing support to members of the Armed Forces described in paragraph (1).

(b) Secretary Concerned Defined- In this section, the term `Secretary concerned’ means–
(1) the Secretary of Defense with respect to matters concerning the Department of Defense; and
(2) the Secretary of Homeland Security with respect to matters concerning the Coast Guard.

SEC. 3. TERMINATION.
Appropriations and funds made available and authority granted pursuant to this Act shall be available until whichever of the following first occurs: (1) the enactment into law of an appropriation (including a continuing appropriation) for any purpose for which amounts are made available in section 2; (2) the enactment into law of the applicable regular or continuing appropriations resolution or other Act without any appropriation for such purpose; or (3) January 1, 2015.

Passed the House of Representatives September 29 (legislative day September 28), 2013.

The relevant portion to the argument as to whether death benefits are covered is Section 2, part (a)sub 1. This is rendered in bold above for easy reference. The key here, I believe, are the words “pay and allowances“.

“Pay and allowances” are described on the Military Pay page of the Defense Department. Pay includes Basic Pay as well as extra pay for various type of duties. Allowances are provided for specific needs. For example, food or housing allowances are provided as needed. A separate benefits page describes various benefits such as the death gratuity to survivors and survivor benefits.

I think there certainly can be a case made that Congress thought they were providing this benefit but the way I read the law, this appears to be inadvertently omitted and unlikely to be up to the discretion of the Secretary of Defense. (Some claim the administration has discretion here but I don’t see it.)

Although the government failed the families of soldiers who died for the United States, it is good to know that a private foundation has stepped in to help until the United Staes government gets its act together. (Read the story on CNN.