I'm not so sure that the action has been so one-sided and that the Russians are desperate with regard to time. Pick your own perception in the fog of war.
Time is very much against the Russians. There was a video about Russian supply logistics posted here a few days ago. Russian war planning is very heavily dependent on the Russian rail network. When they get off the Russian rail network, they are dependent on trucks. They started the war with enough trucks to move about 3000 tons a day. Enough to support maybe 1/3 of the force they have in the country. A large number of those trucks have been destroyed or are stuck in the convoy going nowhere.
There have been trainloads spotted in Russia of civilian trucks painted with the 'Z' symbol. They are so desperate they are pressing civilian trucks into combat.
They are also critically short of fuel tankers and the Ukrainians have been hunting those. They have already lost 60+.
Another problem the Russians have is they skimped on tires. All their non-tracked vehicles have cheap Chinese tires that are not rated for the loads they have been required to carry. These vehicles have also been stored outside in Russian winters for a few years, so the rubber has aged. They are suffering from blown out tires all over the place and they don't have enough spares.
I think that Putin just does not care. He has his troops slaughtering civilians and committing war crimes on a daily basis. What does he care if they do that 2 weeks or 6 months. Can they survive next winter...I doubt it. I expect things get very interesting by this fall.
Things will likely get interesting in a few weeks. The full force of the sanctions are going to hit home in the next couple of weeks. The economy will go into chaos and that will probably result in increased protests. The protests could exceed the ability of the police to control them, and with the army entirely committed to Ukraine, there will be no troops to put on the streets.
The army's supply problems are bad and likely to just get worse along with the casualties mounting. The Ukrainians estimate about 10,000 dead now. That's 5% of the invasion force. If that's true and the losses remain steady (they are likely to go up from disease, starvation, and improved combat ability of the Ukrainians) that means the entire army will be dead in 20 weeks.
That's not counting the wounded. The wounded are usually about 3-6X the dead, which means that they could have 40,000 troops out of combat due to being wounded. That would give them another few weeks before they are out of troops.
This is quite possibly the worst planned and executed military operation I have ever seen. And I've been studying military history my entire life.
Ironic that Russia has adopted an incomplete and lost Swastika as a symbol of this idiotic invasion.
The symbols are an indicator of the type of unit:
"Letter “V” Russian Marines
Letter “Z” Eastern Military District
Letter “Z” Southern Military District
Letter “O” units from Belarus
Letter “X” kadyrov
Letter “A” Spetznas"
The Eastern and Southern Military Districts troops are making up the bulk of troops, so that is the most frequently seen symbol.