Washington has already ordered two rounds of sanctions against the ruling junta if it continued to ignore calls for a democratic transition.
Last week, Mr Bush warned that failure to release Nobel peace laureate Aung San Suu Kyi and other detainees could trigger USled efforts to tighten international sanctions on the regime.
The House of Representatives, at the same time, voted to bestow Ms Suu Kyi with the Congressional Gold Medal - the US Congress' highest civilian honour.
'It will be very difficult, no matter whether in Texas or Singapore or elsewhere, to persuade the President to sit down with the junta leader who used force to kill demonstrating monks and their movement for freedom,' explained Mr Douglas Paal, a former Bush administration official and a seasoned Asia hand.
'Symbolically, to meet Burma's leader or even his junior representative will disappoint the hopes of the people of Burma.'
A White House insider disclosed that the real momentum against Myanmar comes from the President's wife Laura Bush, 'who will put her foot down again and again against a Burmese leader entering her house'.
Mrs Bush, who has been influenced heavily by her husband's cousin, Ms Elsie Walker, a proponent of freedom for Tibet and Myanmar, charged on Tuesday that Myanmar's junta had not enacted even 'minimal' democratic reforms.
'The junta has made no meaningful attempt to meet and talk with democratic activists. Instead it has continued to harass and detain them,' she said.
In the face of such pressures, sources revealed that Washington has made it clear that it will not convene any summit with Asean unless there are significant changes on the ground in Myanmar.
This has put Asean in a difficult position.
'When the Americans extended Asean the invitation to the Crawford Ranch, they assumed that we would take a strong position on Myanmar by now,' said an Asean diplomat speaking on condition of anonymity. 'This has not been the case seeing how Myanmar got its way in Singapore.'
At the Asean summit in Singapore last month, the grouping's leaders had to abruptly withdraw an invitation to UN envoy Ibrahim Gambari to address Asian leaders after Myanmar objected.
If the Texas summit is cancelled, it would be the second time that Mr Bush has scrapped talks with Asean leaders.
In May, he had agreed to attend a summit highlighting 30 years of official ties between Washington and South-east Asia in Singapore on his way to the Sydney Apec talks but cancelled at the last minute due to the Iraqi crisis.
US Secretary of State Condoleezza Rice also did not take part in two Asean annual meetings, in 2005 and this year. It only served to bolster the view that the region was now on the backburner in Washington - a perspective that the Bush administration has refused to accept.
Asked whether the President would host Asean leaders at his Texas ranch - known as the Western White House and reserved for a select band of world leaders - a White House official said: 'We continue to discuss the issue with Asean officials, but there is nothing to announce at this time. The fact that the President issued the invitation speaks to the importance we place on our growing ties to the region.'
The Asean diplomat noted that if indeed the summit was called off, Asean leaders might still try to get together with Mr Bush - most likely when he attends the Beijing Olympics to be held from Aug 8 to 24.
'By then, the whole notion of commemorating a 30th anniversary will lose its significance because we will be a year late,' he said.
'And Myanmar could still be a thorn in the side then. Wherever the venue, Bush has no plans to be in the same room with the junta leader.'