Any amendment requires a 2/3 vote of both houses of Congress for approval. Tacking that onto the debt ceiling bill will just be seen as a "poison pill" designed to make it LOOK like the GOP is trying to do something, but deliberately sabotaging it. The BBA was always going to have to be passed seperately.
Article V of the Constitution specifies that if the legislatures of two-thirds of the states petition Congress for a constitutional amendment on the same subject, then Congress must call a convention for proposing that amendment. Between April 29, 1975 and January 29, 1980, 34 petitions from 30 different state legislatures were submitted to Congress on the subject of a Balanced Budget Amendment.
The participating states were Alabama, Arizona, Arkansas, Colorado, Delaware, Florida, Georgia, Idaho, Indiana, Iowa, Kansas, Louisiana, Maryland, Mississippi, Nebraska, Nevada, New Hampshire, New Mexico, North Carolina, North Dakota, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, and Wyoming.
Since 1980, two additional state legislatures have petitioned Congress for a convention for a Balanced Budget Amendment, bringing the total number of participating states to 32.[10] If two additional state legislatures were to petition, then the required two-thirds majority of states would be reached (34 out of 50 states) and some contend that Congress would be required to call a convention to propose a Balanced Budget Amendment. In December 2008, the Ohio legislature considered making Ohio the 33rd state to petition for a convention on the subject, but decided against it.