I'm not sure if the problem facing the Jordanians is political in nature, nor one of commitment.
The one time that Syrian and Jordanian forces met in the field during 1970, the reinforced Syrian 5th division, with up to 300 T-55s, encountered Jordanian units consisting of the 25th Infantry and elements of the 40th Armoured brigades (about 100 Centurions, IIRC) around ar-Ramtha. The Jordanians were occupying two ridges blocking the Syrian advance. The Syrians stumbled into them, and attempted to force their opponents off the heights. The Syrian attack was filled with errors (lack of coordination between infantry and armor, tactics involving all the subtlety of a bull in a china shop), but the Jordanians pushed out of their positions and forced to retire. Instead of, say, flanking the Syrian advance and counterattacking, the Jordanians just let the enemy come to them, failed to make even basic maneuvers, suffered loses in material at a ratio of 2:1, and in the end failed in their task. Though the core of the Jordanian forces was relatively intact, the invasion was halted by air attacks which sapped Syrian morale, not any feats of arms on the ground.
So, what lessons can we take from this? The Syrians are by no means going to perform brilliantly. Rather, they are going to attack in a very straightforward manner, and the Jordanians are going to sit there and let the Syrians come. And, given the Jordanian performance, such a battle is going to develop into some sort of slogging match in which Syrian numbers will wear down the Jordanian forces. The Syrians will have issues, but unless their opposition can improve its abilities on the battlefield, Syria just might stumble into Amman.