Then I'd say you have the wrong interpretation of what Art 1, Sect. 9, clause 6 says.
Breakdown:
"No money shall be drawn from the Treasurey..."
Clearly defines what repository Congress shall drawn funds to finance the bills it passes and are subsequently made law.
"...but in consequence of appropriations made by law..."
A clear stipulation that the only time Congress can "withdraw" money from the Treasure is when a specific law calls for such financing as per bills passed by Congress and subsequently made law by approval of the President.
About the only thing I believe you got right in your post above is the periodic requirement for Congress to report on what they spend.
I don't know where you get the idea that anyone has stated that the government is being forced to spend money. I AM, however, saying that if Congress passes a law that has appropriations (funding) affixed to it, Congress must, by law, fund that program. Now, maybe they don't fund such-and-such program 100% or perhaps not to the levels it once was a year or two ago, but where appropriations is required by law, I don't think Congress can ignore providing funds for it. Two examples of what I'm talking about:
CPB/NPR. Right now, there's a battle in Congress not merely on how much to reduce funding for public broadcasting, but to defund public broadcasting entirely. If the law that ushered in CPB/NPR requires appropriations, then by law Congress cannot ignore funding it. Furthermore, unless there is a specific fixed amount the law states must be applied toward public broadcasting, Congress can reduce the amount of money that goes to it, but it cannot defund public broadcasting, not without changing the law.
Medicare/SS/Medicaid. These programs are mandated by statute for two reasons: 1) Medicare/SS are "the people's safety net" programs. WE fund them via withdraws directly from OUR income. So, Congress must fund these programs. 2) Medicaid is a partnership between the federal government and the States. As such, Congress must also fund Medicaid by statute. How much goes to fund these permanent programs is also something that needs to be hashed out by Congress, but these programs must be funded by law. Congress can't ignore providing for them if they wanted to.
Based on a strict interpretation of Art. 1, Sect 9, clause 1, I believe it is unconstitutional for Congress to shut down the government even partically if it cannot approve a budget. It can approve continuing resolutions via House rules until the next fiscal year if Congress can't reach an agreement on a spending bill (budget), but with every CR comes more unrest and uncertainty. Still, I'd rather they do that than to shut down government in whole or in-part.