Firstly, how far behind on rent are they?
Have you sent them notices in writing about late rent, and if so how many have you had to send?
How often do they say they are going to do things (like pay overdue rent) and they never do?
To tell you the truth IMHO, if they are starting to be regularly late in rent payments and they don't do things they say they are going to do - then it is time to evict them.
In NSW Australia, if the tenant is more than 2 weeks late in rent, and prior to them reaching 2 weeks late you have called them asking for late rent and sent notices, you can evict the tenants. If the tenants do not leave you can apply to the Tribunal to get them out and ask for outstanding money to be paid to you.
However, if it does get to this stage, the tenants may be pissed off so may do some damage to the property in retaliation. Then you have to go back to the Tribunal to get the Tenant's Bond (Security Deposit) and any other funds to repair any damages done to your place.
The longer you leave it the worse it will get. We had some tenants similar to this which we finally got out earlier this year. They would say they would pay rent due by the end of the week and no money would come by the end of the week. We took them to Tribunal and got them out, and we got the Bond plus unpaid rent and other money for damages and leaving the place dirty (over and above the Bond) awarded to us - just under $4K.
The tenants said they couldn't pay and so went on a payment plan to pay about $135 every 2 weeks. They didn't pay any of the payments, so then we went to the local court to get a sheriff to go to their new place and take their property. The must have gotten scared from this because they approached the local court and agreed to pay $60 per week. We have currently received about 10 payments so it will be a long time before we get all our money back.
As I said the longer you leave it the worse it can get. You should also look at improving your criteria for selecting new tenants. I have given an answer to this question How to choose a good tenant as a private landlord? Hopefully it can give you some ideas of what to ask for when searching for your next tenant.
Update due update in Question
Six weeks behind in rent is quite a bit to be behind. If the landlord had been asking the tenant to pay the late rent during this period and the tenant had been giving excuses why the rent was late and saying they would pay it by a certain time but never did - it is a big sign that they will tell you lies.
If this is the first time they have been late in paying rent and now they are back up to date with the rent, you might want to give them one more chance.
If this is a pattern that happens regularly it is better to get them out, as it will happen again, you will get in an argument with them and then they might stop paying rent altogether.
You can usually gain a better perspective of the tenants from their action rather than their words - that is why ascertaining their past rental history is so important when finding a new tenant.