This is a bit of difficult question to answer, as it depends on when we decide the rise of the Pippinids began. There is a strong argument to be made that through the death of Pippin II in 714, the family did not represent an existential threat to the regime. Though powerful, he himself was subject to the checks and balances of palace culture that underpinned the stability of Merovingian rule. In many respects, he was not substantially different from other mayors and regents who had negotiated factional politics over the last half-century during a string of child and short-lived kings-- he just happened to be particularly successful.
Merovingian political culture was centered on the palace and person of the king; magnates at court would vie for political and ecclesiastical office, derived from royal authority and proximity to the king. The willingness of the magnates to participate and compete in this system formed a broad consensus that lent stability to the Merovingian regime. Magnates invested in the system would cooperate and mobilize against peers that threatened or attempted to control access to the king to the detriment of the assembly. The result was a stable political system that was invested in the continuation of the Merovingian line.
Mayors emerged over the same time period as powerful negotiators between the king and palatine magnates, particularly at a palace complex with a child king or that lacked a king altogether. After the death of Dagobert I (d. 639), there is a greater frequency of child and short-lived kings, which allowed greater space for mayors and regents to shape palatine politics. Mayors operated in a precarious position, however, and we should not assume a supremacy that would later become characteristic under Charles Martel. A mayor that overstepped his bounds would be met with swift opposition, as was the case with Grimoald, son of Pippin I and mayor of the palace in Austrasia. Following the death of Sigibert III, Grimoald elevated his own son to the throne, who he claimed had been adopted by the late king, and exiled the obvious heir Dagobert II to Ireland. It is possible that he was in league with the queen-dowager Himnechild, who was not the mother of Dagobert, and perhaps in an attempt to secure her continued influence planned to marry her daugher to Grimoald's son.
Grimoald, however, had overstepped his bounds. After a short reign, he and his son were ousted from power, and falling into Neustrian hands, Grimoald was executed in 657. Despite being the ancestor of the Carolingians, Grimoald was still subject to the rules of Merovingian political life. While the mayors were leading political men among the kingdom's magnates, they did not represent a threat to the long term stability of the regime. We should be careful not to read the later success of the Carolingians backwards onto the seventh century. The Pippinids were a powerful family, but their fortunes could and did rise and fall. There is nothing to suggest that the family might one day depose the Merovingian line.
Even when Pippin II (d. 714) accumulated what might be labeled an unprecedented amount of political clout, rooted in his military success and advantageous marriages, he was still subject to the palatine culture that made his position possible. Pippin was careful not to pack the Neustrian court with his own Austrasian followers, which had led to the demise of Childeric II twenty years prior, and was even blocked from attempts to gain access to St.-Denis, a premier Merovingian monastery. While the protagonism of the king had waned (most were minors and young adult) in the closing decades of the seventh century, the contemporary king of Neustria, Childebert III (d. 711), was no slouch, and there is solid evidence to suggest that even he was a political protagonist in his own right. Pippin and his family were powerful and perhaps even viewed as too powerful, but there is no reason to suggest that the Pippinids were viewed as threat to the existing political structure or regime.
Even when Pippin II died in 714, the self-correction of palatine politics meant that a regime change was not inevitable. Pippin's son Drogo had died in 707 and in 711 his other son Grimoald had been murdered. When the family attempted to install Pippin's grandson as mayor, the Neustrian magnates had had enough and ousted the family from power. It would fall to Charles, a marginalized son of Pippin's second wife, to pick up the pieces and re-forge Pippinid power in the Frankish realms. The in-fighting that would consume the Frankish realms following Pippin's death was not unusual, and was in fact part of the structure that helped perpetuate Merovingian legitimacy. However, when Charles Martel emerged as the undisputed premier magnate of the Frankish realms, things had indeed changed, to the extent that Charles would be able to rule for five years at the end of his reign without a king.
The Merovingian response to Charles Martel is difficult to ascertain-- in fact, how exactly kings felt about their declining role in the administration of the realm is frustratingly absent. While those invested in the Merovingian regime had previously been able to counteract the ambitions of politically powerful families who attempted to overreach, Charles Martel managed to take advantage of a political culture that had fragmented considerably following 714, and was able to consolidate his own position within the balance of power, staffing political offices with his followers. Resistance to his rule, however, was not unopposed, and while he would control the better part of Neustria and Austrasia by 719, he would spend most of the next two decades bringing unwilling magnates into line.
This response has purposefully avoided the opinions of individual kings on the rising power of the Pippinids at the start of the eighth century, and has instead focused on the reaction of the larger political culture to magnates who sought power at the expense of their fellows. For the most part that is because Merovingian kings had largely lost the ability to be administratively proactive (largely due to that series of child rulers), even when someone other than the Pippinids controlled the mayoral office. Exceptional power was cause for concern within the aristocratic assembly, but it did not itself threaten the existence of the family line. The usurpation of Merovingian authority, is more a feature from the reign of Charles onward, and reflects a changing political culture increasingly willing to deal directly with him and his descendants, ultimately sidelining the Merovingian family. While the latter would retain a symbolic role as the kingdom’s necessary traditional source of legitimacy, the Carolingians would continue to accumulate military power and prestige as religious reformers. When Pippin III was crowned in 751, there appears to have been little resistance among the Franks.