The Constitution is exactly what gives the Senate the power to establish its own rules. Article I, section 5.
How I wish Congress would keep to the Constitutional minimum of Article 2 Sec 4 Par 2.
Yes ... and No. They are bound by the enumerated powers, or they would be if they wanted to govern under the Constitution. The TARP/Bailout/ObamaCare bills are so far beyond their lawful authority that I don't think we can pretend the socialists in our Congress are following Article I, Section 5. They are quite clearly grabbing power and nothing more.