It is believed that when Lord Vishnu took the avatar of Venkateshwara Swamy, the goddesses (Lord Vishnu's two wives) gave seven curses to Him. For each curse, Lord Vishnu took one step back from them and at last became a statue which is in Tirupathi.
What were those seven curses by which Lord Venkateshwara became a statue?
The Seven curses by the goddesses to Lord Vishnu seems to be untrue for sure.
I will provide the list of arguments in favor and the facts that are in against the incident of curses by goddesses.
Arguments 1,2 are in favor to the incident asked in question. Although the two arguments are in favor, they do not mention the curses by goddesses at all.
Facts 1,2,3 favors to the conclusion that both events: Curses by goddesses, no knowledge of Lakshmi about marriage of Padmavathi and Venkateswara in prior are false.
A famous Telugu movie named Sree Venkateswara Mahathmyam(1960) showed an incident in which Lakshmi come to know about marriage between Padmavati and Venkateswara and gets upset. Then Venkateswara becomes statue after failing to control them. You can read it from the Wikipedia article of the movie.
After the marriage, Sage Narada informed Lakshmi about the wedding, then fuming, Lakshmi confronts Vishnu. The clash between his two consorts leads Srinivasa, to turn himself into stone form.
The same incident has been mentioned in the original website of Tirumala citing no authentic references for this particular story. But they mentioned that The “Temple Legend” is made out of references from a range of ancient scriptures such as Varaha Purana, Padma Purana, Garuda Purana, Brahmanda Purana, Markandeya Purana, Harivamsa Purana, Vamana Purana, Brahma Purana, Brahmottara Purana, Aditya Purana, Skanda Purana and Bhavishyottara Purana. The story has been mentioned under the subtitle LORD SRINIVASA TURNS TO LORD VENKATESWARA
In about six months after this celestial marriage, Goddess Maha Lakshmi who left the lord, in the past in a huff after sage Bhrigu kicked Lord Vishnu on his chest, her dwelling place, came to know that her husband married again and came to see him in disbelief.
It is said that the Lord turned himself into a granite statue right in front of his two spouses when they together encountered him over his remarriage. Lord Brahma and Lord Shiva then appear before the confused queens and explain the main purpose behind all this complex episode, the Lord's desire to be on the holy seven hills for the emancipation of the mankind from the perpetual trials and tribulations of Kali Yuga. Goddesses Lakshmi and Padmavathi also turn into stone idols expressing their wish to be with their Lord eternally. Goddess Lakshmi stayed with him on the left side of his chest while Goddess Padmavati rested on the right side of his chest.
Note that both the arguments does not have any mention about the curses. But both of them supports that Lakshmi does not know about the marriage of Padmavathi and Venkateswara in prior.
This fact clarifies that certainly the first argument (and possibly the second argument) is/are false. It says that the clash between the two consorts is an invention by the Pullaiah, who is both the Director and the producer of the Sree Venkateswara Mahathmyam movie.
There is an interesting story behind the last scene of the film. After collecting the story material Director-producer Pulliah asked Ramireddi to write the dialogue for the sequence in the last scene in which both Sri Lakshmi and Padmavathi contend for the right to be the spouse of Srinivasa in his presence. Srinivasa, vexed with this quarrel turns into stone. This is not found in any of the source material. It was Pullaiah's invention. Without being aware of it, Ramireddi went ahead with the dialogues according to the wishes of his producer. The dialogues were indeed very effective. Later, however, Ramireddi was astonished when he was told that the scene and the episode were Pullaiah's creation!
Varaha Purana mentions that Lakshmi knows about the marriage of Padmavathi and Lakshmi in prior. Lakshmi and others prepares Venkateswara for marriage. So there is no concept of ignorance to Lakshmi regarding the marriage
అంత శ్రీనివాసుడు ప్రియభామినియగు లక్ష్మిని బిలచి “కల్యాణి! వివాహము కొఱకై యేమి చేయవలెనో తెలుపుము. నీ చెలిమికత్తియల నాజ్ఞాపించి అర్హనమగు కృత్యము నొనరింపుమ”ని కోరినంతనే శ్రీదేవి చెలిమికత్తియల ప్రేరేపించెను.
(After Padmavathi got ready)Then Srinivasa invited Lakshmi and requested "Kalyani, tell me how to get prepare for marriage. Please order your companions to do the preparations to be done". Lakshmi, then, immediately ordered her companions accordingly.
[1-2, Chapter 8, Uttarabhaga, Varaha Purana]
According to the Bhavishyottara purana, Venkateswara informs to the Lakshmi about the marriage with Padmavathi in prior. Hence, it reconfirms that both the arguments 1,2 are false, if nothing dramatically happens afterwards.
శ్రీనివాసుడు లక్ష్మి దేవితో- లక్ష్మీ! నాతో నీవు రామావతారమున చెప్పిన నంగతిని తలంచుకొనుము. వేదవతీ వివాహ సమయ మేతెంచినది. ఈ కలియుగమున నీ సమక్షముననే పద్మావతిని వివాహమాడ గోరుచున్నాను. ఇట్లు శ్రీనివాసుడు చెప్పుచుండగనే శ్రీదేవి “శ్రీనివాసా ! వేదవతిని యథాశాస్త్రముగా పరిణయ మాడుమ”ని తాను మున్ను పలికిన మాటను తలంచి తప్పక నా మాటను సఫలపరచుమని ప్రార్ధించుచు సంతోషముతో శ్రీనివాసునికి నమస్కరించెను. శ్రీమన్నారాయణుడు లోకమాతయగు శ్రీదేవిని సంతోష చిత్తుడై ఆనందపరచెను. `
Srinivasa told to the Lakshmi devi "Lakshmi, remember the words told by you during my Ram-avatar. The time for marrying Vedavathi has been come. I am willing to marry Padmavathi infront of you in this Kaliyuga." In between the conversation Sri devi told "Srinivasa, Marry Vedavathi according to the scriptures". Then saluted and prayed Srinivasa with happiness to follow the same words told by her after remembering her words during Thretha yuga. Srinivasa then made Lakshmi happy.
[198-201, Chapter 10, Bhavishyottara purana]
Thus according to the puranas, Lakshmi is aware of the marriage and allowed Venkateswara to do so. Along with these, no purana, afaik, has any mention regarding the incident in question. The only ambiguity now is whether argument 2 has any scriptural basis. If we go by fact 1, 2, and 3 then it will be obviously false. Still, if one thinks that there is any little chance of curses by goddesses or ignorance of Lakshmi regarding marriage of Padmavathi and Venkateswara, then Harivamsa Purana can be a potential source.
https://ia800300.us.archive.org/2/items/historyoftirupat035504mbp/historyoftirupat035504mbp.pdf