It's very hard to give a short answer to your question. I should say that I come to this from a left wing perspective, so you need to take that into account 
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BUT, it is fair to say that very many respected economists who are middle of the road politically would agree that it is very easy for misdirected efforts to cut a budget deficit too fast to result in either recession or reduced growth, and therefore actually to make it harder in the medium to long term to balance the budget.
To put it simply, it's what happened in the 1930s, there was a crisis, governments slashed spending, that threw lots of people out of work, they had no money to spend and the end result was a downward spiral into depression.
Other questions to ask are:
(a) what is the actual day to day impact of running a budget deficit in this country at this moment, and is that deficit sustainable - eg in Greece it clearly wasn't as the country could no longer borrow, largely because the country has a very long history of defaulting on its debts, whereas the UK does not (in the book This Time is Different analysing the crisis, the last 'government default' in the UK that the authors came up with was Henry VIII appropriating the resources of the monasteries). Obviously it's not ideal to have a very large national debt (which an annual deficit will add to) because you have to pay interest, but the UK has had much larger debt to GDP ratios in the past at times when national income was lower. (This page is quite useful to show the deficit in context)
(b) why do we have a deficit? Obviously it's complex, and the financial crisis is a significant part of it, but recession will always increase a deficit - unemployed people are not working, paying tax, and generating resources, under employed factories or businesses that go bust ditto. Growth is generally the best way to get out of this.
Spend your time reading the Financial Times, International Monetary Fund reports and the like (ie not left wing propaganda!) and I think you'll find it pretty clear that cutting public spending as is current government policy is not an effective way to reduce the UK deficit.
Not only that but the things that are being cut are such a minimal part of public spending that cutting them won't even have much of an immediate impact. Jobseekers allowance for example made up 0.007% of public spending in 2011-12 (sorry old figs, but the %ge doesn't change much from year to year).
Obviously, it does fit with wider Conservative policy to reduce welfare spending - but that is a political and not an economic decision.
Sorry for the essay!